As you mention, right before the Enterprise travels back in time, we do see an assimilated Earth, so yes, assimilation still was their primary goal. My question still remains as to why the Borg chose that particular point in time. Assimilating Earth in the 1980's, say, would have ended in the same result as assimilating Earth in 2063.
No, it wouldn't, because Earth's technology would've been less advanced to them and thus less worth assimilating.
Remember: The Borg do not create. They take what others have created. They couldn't turn a pre-technological world into a Borg world, because there isn't enough tech for them to absorb/adapt. They needed to assimilate Earth at a point when it would've had enough advanced technology for them to use as raw material.
Why does disrupting first contact with the Vulcans have anything whatsoever to do with their ultimate goal?
As I already said, my proposal is that they chose that point because it was the point that Earth became warp-capable and thus the earliest point when it was advanced enough to be worth assimilating. Of course, that's a stretch, because a world with only one functioning warp engine isn't all that useful to them. But in order for that one engine to exist, all the necessary technological ingredients and industrial infrastructure to build more must've existed too, despite the way the film portrayed Cochrane's operation as small and ragtag.
But they were trying to prevent First Contact. So how does that help them assimilate what they want in the future if Earth never becomes the Federation's primary world?
Exactly my point. The premise of the film falls apart if you examine it too closely. I'm just suggesting that what they chose was a compromise position between removing the Federation as an obstacle and gaining enough useful biological and technological distinctiveness from it. In order to achieve the former, they had to sacrifice some of the latter, but they chose a late enough point that they didn't sacrifice too much of it. It's not a very convincing handwave, but it's something.
What I proposed in DTI: Watching the Clock was that the Borg were manipulated into this out-of-character operation by the Sphere Builders, as a third attempt to defeat the Federation and clear the way for their invasion after their attempts in the 26th and 22nd centuries failed. They used the Borg as a scapegoat so the Temporal Agents wouldn't identify their involvement and stop them. So it wasn't entirely the Borg's idea. But it would've still needed to be something that would make sense to the Borg as something that served their needs.