Also it would be interesting to know what Sam Peeples (who wrote WNMHGB) and the TOS writers thought in terms of the galaxy's shape and size. Certainly at best they only had a 1960's understanding of the Milky Way and not our current understanding from more than forty years of research since.
Interesting question about 60's understanding.
From my 1968 printing of the Columbia Viking Desk Encyclopedia:
"Milky Way system, the GALAXY which includes our sun. It comprises c.50-200 billion stars in the form of a disk; at its greatest diameter is c.100,000 light-years; thickness c.10-16 thousand light-years. Solar system is c.30,000 light-years from center. Position of earth permits observation of numerous stars appearing to form white pathway (rim of our galaxy) commonly called Milky Way."
Also, it does take "days" to go from star to nearby star at warp elsewhere in Trek. Go from FTL to STL, and this distance in lightyears will translate to a trip duration in years - and the distance from a star to its not-quite-closest-neighbor does tend to be less than ten lightyears.
Also, "years" is a valid expression for "decades"... Although there would be some poetic harmony in the "days"/"decades" pairing, too.
We know that warp speed to actual speed is variable in TOS. Slow actual speeds in system near stars and planets and fast between star systems. ~1,000 LY per day for "Obsession", "That Which Survives" and "Breads and Circuses" are quite reasonable going between systems.
As to Kirk's log entry:
Captain's log, Star date 1312.9. Ship's condition, heading back on impulse power only. Main engines burned out. The ship's space warp ability gone. Earth bases which were only days away are now years in the distance.
The reason I think it is an interesting indicator are based on several things...
1. He compares the time difference between "days" to "years". A 1,000 LY trip in days is on the order of 400,000c. If impulse was limited to sublight, it wouldn't be "years" but "thousands of years" like how he compared the trip to the Andromeda Galaxy in "By Any Other Name".
2. The Enterprise's five year mission has enough food to last a crew of 430 for five years (surprise!) according to "The Mark of Gideon". If the flight home is at sublight, they'd run out of food and Kirk's log entry would reflect their dire situation.
3. In "Miri", Kirk says, "We're hundreds of light years from Earth, Mister Spock. No colonies or vessels out this far." This would suggest that Earth colonies and likely bases were limited to a radius of 1,000 LY from Earth. If that's the case and if Earth is 20,000 LY to the rim according to 1968 thinking then the nearest Earth base is roughly 19,000 LY away. That's a pretty long trip home!