I'm giving this more thought than it deserves, obviously
Hey, it's Star Trek, and "The Motion Picture" at that. You can never give these things enough thought.
Keep in mind that we don't even know that V'ger is traveling at warp speed, at first. There's nothing to suggest that the Klingon encounter occurs at warp speed. Nor would its mission necessarily be facilitated by constant warp-speed travel. The only direct dialogue reference to V'ger's warp capability is when Sulu says "Starfleet reports forward velocity has slowed to sub-warp speed. We are three minutes from Earth's orbit." Indirectly it's suggested by Kirk's dialogue in the rec deck scene when he says it's 53.4 hours away from Earth. But V'ger could have gone to warp speed only when approaching Earth.
Well, I've always had the sense that V'Ger is "racing home" and has been doing so a while. While the fight between V'Ger and the Klingons may appear to be occurring at a sedate pace, at sub-light speeds, bear in mind that motion and velocity are relative things. There is no way to properly judge whether they are duking it out at sailing-ship speeds or caught in each other's warp bubbles (though I prefer the latter). Later on, the Enterprise is meant to penetrate V'Ger's warp bubble, meaning that both ships are at warp with respect to the surrounding spacetime fabric, but not at warp relative to themselves.
To close in on a particular thing you said there:
Nor would its mission necessarily be facilitated by constant warp-speed travel.
To quote our wonderful TMP-loving friend
FcukTWOK:
V'ger likely analyzed the visible universe during its trip across the Milky Way via remote sensing. If it was still in contact with the Machine Planet during its voyage it could have employed some form of subspace VLBI (with a baseline maxing out at ~60,000ly) to vastly increase imaging resolution. Furthermore, the synthetic aperture effect caused by its motion through the galaxy would have boosted it even more. Applying assumptions of cosmological mediocrity and isotropy, there would have been absolutely no need for V'ger to have directly patterned extragalactic objects to generate a sufficiently isomorphic internal model of the global spacetime manifold for the machine to perceive that there was, indeed, something beyond it.
In other words, we can assume V'Ger has extraordinary data-gathering abilities, and not only would being at warp not impede those abilities, but it may even
enhance them.
Yes, detection of a planetary body by occultation takes a long time to verify. But the AU-scale V'ger wouldn't necessarily be transparent to light, and could be presumed to be denser near its core. (And where is it stated that the core is smaller than our Moon?)
Although V'Ger would probably be denser nearer its core, where the central vessel is located, its core -- if defined by the vessel itself -- is considerably smaller than our moon.
From
V'Ger's Memory Alpha entry:
The size of V'ger's vessel has also been a subject of debate. In dialogue cut from the theatrical version of the movie, Decker says the spacecraft was seventy-eight kilometers (forty-eight miles) in length. The novel adaptation of the film gives the same dimension for the ship and states it as displacing six million times the amount of space as Enterprise. One popular non-canon site for Star Trek technical details, the Daystrom Institute Technical Library, listed V'ger's overall length at a staggering ninety-seven kilometers, stated as being determined from apparently careful measurement of the image of the refitted NCC-1701 from the movie's scenes, as the Enterprise traveled closely (at only five hundred meters distance, from the movie's dialogue) over the various parts of V'ger's exterior structures, during the Federation starship's initial close examination of the "intruder" vessel. Another estimate places V'ger's colossal length at a much more conservative twenty kilometers instead, possibly based on the statement of replacement navigator DiFalco's "distance inside the intruder as seventeen kilometers," spoken just after Chekov reports that V'ger's "orbiting devices" were eighteen minutes from reaching their equidistant deployment points in Earth orbit, during the approach to Voyager 6's "island," in the most extreme part of V'ger's interior that the Enterprise was allowed access to. The latter estimate, however, would make V'ger impossibly smaller than the roughly seventy kilometer-long Whale Probe featured in Star Trek IV: The Voyage Home, given that the latter was passed by a Federation starship within minutes, rather than the near-hour it took to traverse even half of V'ger at a faster pace, much of which was carried out at only a half-kilometer distance from the "intruder's" hull.
So we have four different sources offering four different size measurements. Even if you take the largest of those measurements (97 km), that is still
an order of magnitude smaller than the diameter of our moon, which is measured at 3,474 km. V'Ger might be a beast next to the Enterprise, but it is still a minnow compared with our moon. Ergo, based on the craft alone, it would be impossible to observe occultation effects with present telescope technology.
You could maybe get something on the cloud, but as I said earlier, that would depend on how luminous it is and its overall opacity. And the answer might be: not very.
Another assumption there is that the cloud's luminosity stays constant. Some stars undergo extreme variances in their luminosity, and I don't see why V'Ger couldn't do the same. The same for its size and extent. There's no reason to assume they remain fixed. Indeed, given that the cloud surrounding the vessel dissipates when the craft makes its final approach toward Earth, it may be the case that the cloud is holographic, or can be retracted in some fashion. V'Ger could just be the "frilled-neck lizard" or epic "peacock" of space objects, deploying its immense cloud only on the final leg of its journey. The Enterprise crew is up against many unknowns, and I love the multitudinous mysteries of the V'Ger construct.
