Why is Kirk's "far side of the Galaxy" third hand?
Because he only knows about V'Ger's journey from what Spock told him, and Spock only knows about it from what he saw within V'Ger. V'Ger actually had the experience (primary source), Spock saw V'Ger's account of the experience (secondary source), and Kirk heard Spock's accout of V'Ger's account (tertiary source). Kirk's statement is pure hearsay.
the speed of V'ger tells how far it could have traveled in a year
There is no basis for assuming that V'Ger has a constant speed.
V'ger's identity as Voyager 6 tells the maximum time it could have been traveling
There is no way to rule out the possibility that the black hole flung V'Ger back in time as well as through space. Indeed, time travel is an implicit element of the kind of black-hole displacement being described. This is what I surmised in
Ex Machina -- that V'Ger had been flung back in time several thousand years. It's unlikely that V'Ger could've exhausted its ability to learn about our universe in a measly three centuries.
and the direction it is detected coming from could be assumed to be the direction it always traveled from.
And as I said, that direction -- from Klingon space -- is pretty much exactly opposite the direction it would've had to come from to be from the other side of the Milky Way Galaxy.
And whether Kirk was correct or mistaken, his statement is a part of Star Trek canon to be considered seriously.
The only thing an anecdotal statement proves is what the speaker
believes, or what the speaker wants others to think they believe. And beliefs can be wrong. Beliefs
are wrong all the time. That's the whole reason we have to view individual accounts critically in terms of how close the speaker is to the source of the information. A statement from someone who experienced an event directly (a primary source) is obviously more reliable than a statement from someone who just heard about it at second or third hand. Spock is closer to the source than Kirk, therefore his understanding is more reliable than Kirk's. It's like a game of telephone -- the more people the information passes through, the more it gets distorted. This is why courts of law don't accept hearsay as legitimate testimony.
I don't accept Star Trek space maps as being accurate or valid if they contradict canonical information.
Canon is a fictional construct that evolves over time and has new information added to it. The maps I'm talking about are based on the cartographic assumptions that Rick Sternbach and Michael Okuda made during their time as graphic artists on TNG, and those maps were not only included in their behind-the-scenes writers' references, but also appeared as viewscreen graphics, such as
this map which apparently was seen on a PADD in
Insurrection (though it originally appeared in the
Deep Space Nine Technical Manual). And again, a source such as an official Starfleet map is obviously more reliable than Kirk's hearsay.
Can you make any plausible suggestions for where exactly V;Ger was coming from?
It's a big universe. Take your pick.
It fell into a black hole and was making its way back to its creator, I would assume by the most direct route.
I don't think V'Ger started back immediately. The imperative it was following was, "Learn all that is learnable, and report that information to the Creator." That's two steps. V'Ger probably didn't set course back for Earth until after it had learned, in its judgment, all that it was capable of learning.
Besides, there would've been the problem of
finding Earth. True, the
Voyager record included a map of Sol's position in relation to 14 known pulsars, but the pulsars we know about are all pretty close to us, cosmically speaking. So whether something came from the far side of the galaxy or outside the galaxy, they'd still need to find their way to a point where they could image our local region of the galaxy before they could identify those pulsars. (After all, the makers of the map never intended the probe to get sucked through a black hole; they assumed it'd be in relatively local space for millions of years.) Now, maybe "how to find Earth" is already included in "all that is learnable," so it wouldn't necessarily have to be a separate step, but it'd still take some time to achieve both. That's why I assumed in
Ex Machina that
Voyager 6 had been flung back in time -- 300 years is simply not long enough for all of that.