They mean that you are drastically overthinking something that is inherently meaningless. I'd ask why, but I don't really care.
Let's not forget that the official explanation for Stardates in the TOS writer's guide was based on a mathematical formula that "varies depending on location in the galaxy, velocity of travel, and other factors" - so in the case of TMP I think one could argue that every time the warp drive was engaged then the following Stardates were no longer synchronized with the previous, so there's no way to determine the number of hours passed. EDIT: fixed typo
I think there would have to be regions where (for whatever reason, natural or artificial) it was possible to travel much greater multiples of C than normal. In Arena for instance, they cover a phenomenal distance in pursuit, in seemingly only a few hours!
Better, it was Warp One! Kirk ordered that speed a lot in season 1. They were heading back to "where they were supposed to be", whatever that means. Cestus III perhaps? Maybe it was just a short distance away...
In my post # 12 in this thread I calculated the distance from Earth that various events in Star Trek: The Motion Picture would happen at if the Enterprise traveled at a various speeds in the movie. For example: 2) If the Enterprise in Star Trek: The Motion Picture traveled at warp factor seven on the TNG scale: V'Ger would be 1.2941804 to 3.0089694 light years from Earth when the Enterprise reached it. V'Ger would be 2.8795512 to 3.3474784 light years from Earth when it crossed the Federation border near station Epsilon IX. V'Ger would be 6.2438984 to 10.531393 light years from Earth when Spock started his journey from Vulcan to Earth - which may have been the same time V'Ger fought the Klingons. V'Ger could travel 141,809.82 to 219,805.22 light years in the 300 to 400 years that were the maximum length of its trip back to Earth from the Machine Planet if V'ger was rebuilt and sent immediately after been launched from Earth more than 300 years before. So which star systems might be the one that V'Ger fought the Klingon ships near in the first scene? If the Enterprise in Star Trek: The Motion Picture traveled at warp factor seven on the TNG scale V'Ger might have fought the Klingons at a distance of 6.2438984 to 10.531393 light years from Earth while within a sphere of space claimed by the Klingons around Barnard's Star - 5.978 plus or minus 0.002 light years or 5.976 to 5.980 light years from Earth, or Ross 154 - Distance: 9.60 plus or minus 0.05 light years or 9.55 to 9.65 light years from Earth. The candidate stars and the reasons for selection are below. List of Star Systems: 1) Alpha Centauri A, B, and C. Distance: 4.365 plus or minus 0.007 light years from Earth, or 4.358 to 4.372 (A & B) or 4.2421 light years (C). 2) Barnard's Star. Distance: 5.978 plus or minus 0.002 light years from Earth, or 5.976 to 5.980 light years. 3) Luhman 16 or WISE 1049-5319. Distance: 6.516 plus or minus 0.001 light years away, or 6.515 to 6.517 light years. 4) WISE 0855-0714. Distance: About 7.27 plus or minus 0.13 light years from Earth, or 7.14 to 7.40 light years. 5) Wolf 359. Distance: 7.86 plus or minus 0.03 light years from Earth, or 7.83 to 7.89 light years 6) Lalande 21185 Distance: 8.31 plus or minus 0.01 light years, or 8.30 to 8.32 light years. 7) Sirius Distance: 8.60 plus or minus 0.04 light years or 8.56 to 8.64 light years. 8) Luyten 726-8 Distance: 8.73 plus or minus 0.06 light years, or 8.67 to 8.79 light years. 9) Ross 154 Distance: 9.60 plus or minus 0.05 light years or 9.55 to 9.65 light years. 10) Ross 248 Distance: 10.30 plus or minus 0.02 light years or 10.28 to 10.32 light years. 11) Epsilon Eridani Distance: 10.475 plus or minus 0.003 light years, or 10.472 to 10.478 light years. 12) Lacaille 9352 Distance: 10.68 plus or minus 0.02 light years or 10.66 to 10.70 light years. 13) Ross 128 Distance: 11.03 plus or minus 0.02 light years, or 11.01 to 11.05 light years. 14) WISE 1506+ 7027 Distance: 11.1 plus or minus 2.3 light years or 8.8 to 13.4 light years 15 EZ Aquarii Distance: 11.1 plus or minus 0.1 light years, or 11.0 to 11.2 light years. 16) Procyon Distance: 11.46 plus or minus 0.05 light years, or 11.41 to 11.51 light years. 17) 61 Cygni Distance: 11.41 plus or minus 0.02 light years, or 11.39 to 11.43 light years. So all 17 stars systems are more or less in the right distance for V'Ger to fight the Klingons near while 6.2438984 to 10.531393 light years from Earth. Ecliptic latitude: When the Enterprise leaves Earth to try to intercept V'Ger it zooms past Jupiter, so the direction that V'Ger comes from should be more or less on the ecliptic plane that the planets in our solar system orbit in. How far from the ecliptic plane and the direction that V'Ger comes from could the klingon ruled star be? According to this interpretation the Federation should claim a sphere with a radius of 2.8795512 to 3.3474784 light years around our solar system, and presumably the Klingons would claim a sphere with the same radius around each star they rule. At a distance of 12 light years a radius of 2.8795512 light years covers 13.775 degrees of arc. Any star with an ecliptic latitude of less than plus or minus 13.775 degrees is a candidate for V"ger to pass through Klingon space around it on the vary to Earth. They include: Wolf 359 Ecliptic coordinates Longitude 163.37705221 Latitude 0.22988975 Ross 128 Ecliptic coordinates Longitude 176.86787284 Latitude -0.48045797 Ross 154 Ecliptic coordinates Longitude 281.37975992 Latitude -0.88764382 EZ Aquarii Ecliptic coordinates Longitude 335.46167152 Latitude -6.23470318 At a distance of 5 light years a radius of 3.3474784 light years covers 38.471 degrees of arc. Any star with a ecliptic latitude of less than plus or minus 38.471 degrees might be a candidate, depending on the star's precise distance. These lesser candidates include: Procyon Ecliptic coordinates Longitude 115.78550204 Latitude -16.01989508 Ross 248 Ecliptic coordinates Longitude 109.99090527 Latitude -16.93970830 Luyten 276-8 Ecliptic coordinates Longitude 16.40352624 Latitude -26.18178630 Lacaille 9352 Ecliptic coordinates Longitude 332.68430632 Latitude -27.51179505 Epsilon Eridani Ecliptic coordinates Longitude 48.16776585 Latitude -27.71576387 Barnard's Star Ecliptic coordinates Longitude 270.07913943 Latitude 28.13150268 Lalande 21185 Ecliptic coordinates Longitude 171.75509783 Latitude 35.84152917 Galactic Longitude: V'Ger is also speculated to have been on the far side of the galaxy, probably because of the direction that V'Ger came from. Assuming that V'ger might have passed by a Klingon ruled star that is within 60 degrees of galactic longitude zero, that Klingon ruled star must have a galactic longitude less than 60 or more than 300. Stars within the correct galactic longitude range include: Lacaille 9352 Galactic coordinates: Longitude 5.10084457 Latitude -65.95703046 Ross 154 Galactic coordinates: Longitude 11.30714980 Latitude -10.28446002 Ross 248 Galactic coordinates: Longitude 17.49416953 Latitude 41.44265142 WISE 0855-0714. Galactic coordinates: Longitude 333.98582184 Latitude -5.53787476 Barnard's Star. Galactic coordinates: Longitude 31.29356328 Latitude 13.51255438 Alpha Centauri A, B, and C. Galactic coordinates: Longitude 316.07432269 Latitude -1.06580303 15 EZ Aquarii Galactic coordinates: Longitude 47.07120601 Latitude -56.97976513 Galactic latitude: The direction that V;Ger comes from should also have a galactic latitude close to zero. If v'Ger comes from above or below the galactic plane it might be interpreted as coming from outside the galaxy instead of from the far side of the galaxy. Stars with galactic latitudes of less than plus or minus 13.775 degrees include: Alpha Centauri A, B, and C. Galactic coordinates: Longitude 316.07432269 Latitude -1.06580303 Luhman 16 or WISE 1049-5319. Galactic coordinates: Longitude 285.59031100 Latitude 5.19686525 WISE 0855-0714. Galactic coordinates: Longitude 333.98582184 Latitude -5.53787476 61 Cygni Galactic coordinates: Longitude 82.31971192 Latitude -5.81797579 Sirius Galactic coordinates: Longitude 227.51693537 Latitude -8.43316571 Ross 154 Galactic coordinates: Longitude 11.30714980 Latitude -10.28446002 Procyon Galactic coordinates: Longitude 213.70249473 Latitude 13.01923606 Barnard's Star. Galactic coordinates: Longitude 31.29356328 Latitude 13.51255438 Stars with galactic latitudes of less than plus or minus 38.471 degrees might be candidates, depending on their precise distances, but there aren't any in the group. Conclusion: The star that fits all three conditions is Ross 154, However, at a distance of 5.980 light years or less from, Earth, the distance of Barnard's Star, a degree of arc would be 0.096342 light years. A sphere of Klingon space 2.8795512 to 3.3474784 light years in radius around Barnard's star would have a radius of 29.888 to 34.745 degrees of arc. Since Barnard's Star has a ecliptic latitude of 28.13150268 and a galactic latitude of 13.51255438 V'ger could pass within Klingon space around Barnard's Star from a direction with ecliptic and galactic latitudes near zero. If the Enterprise in Star Trek: The Motion Picture traveled at warp factor seven on the TNG scale V'Ger might have fought the Klingons at a distance of 6.2438984 to 10.531393 light years from Earth while within a sphere of space claimed by the Klingons around Barnard's Star - 5.978 plus or minus 0.002 light years or 5.976 to 5.980 light years from Earth, or Ross 154 - Distance: 9.60 plus or minus 0.05 light years or 9.55 to 9.65 light years from Earth.
My assumption is that Warp 1 or even 2, is a preliminary speed, to "warm up the engines" and probably for safety reasons, especially if they are relatively near a star system or other gravity well. We probably shouldn't assume that the Enterprise was coasting at light speed for more than a few hours at most.
It may hurt my head and make me ask why, but a part of me also loves this and wants to see it on a map. My internal McCoy has the day off but faxed in a suggestion for analgesics.