[lathspell]

At a bare minimum the Ring knew that it had been around Sauron’s primary enemies. They had persistently refused to claim it and refused to allow Sauron's servants (the Ring must have known they were there too) to take it.

Why would the Ring know this? I don't think so at all. The Ring knew that he was born by Frodo, and that there were Nazgûl at hand. I don't believe that the Ring knew more than this, until Sam took it from Frodo at Cirith Ungol. At that point it knew Sam was there as well.

Frodo seems to be the only one who doesn't have some power fantasy about using it.

Don't forget Bilbo, he didn't envisage himself as a great lord. He just thought the Ring was a beautiful and very useful thing. I think that only the ones who are in the presence of the Ring, able to get it, see themselves great and terrible. Once you have obtained the Ring, it is clear that it doesn't make you Samwise the Strong or Lord Smeagol. Although I think that Gandalf and Galadriel and such poweful people would know what the Ring would do to them.
Once you've got the Ring, you'll feel it only as a burden, though you would not get rid of it. And if you didn't know what the Ring was exactly, like Bilbo, you wouldn't even blame the Ring.
Now, the only who doesn't seem to have visions of power when in presence of the Ring is Tom Bombadil. But he is such a mysterious man, and there are already too many discussions about him, that I'm not going to start one about him here.

This has me wondering about the Ring-inspired fantasies of Gandalf, Galadriel, Boromir & Sam, et al. Where do those fantasies arise? Is the Ring putting those specific fantasies into their heads, or are they creating the whole thing themselves - what I mean is, is it a case of 'If I claim the Ring I can do X', so that the power trips are invented by the individual? Which would mean that Gandalf & the rest on some level had thought about doing some such thing anyway. Sam actually had those power fantasies already on some subconscious level, rather than the Ring constructing that fantasy & putting it into his head.

The Ring doesn't plant the fantasies in your head. It seems that, once you know what the Ring is and how powerful and object, you are always tempted by it. If you don't know what it is, you're not tempted. Frodo knew Bilbo had the Ring, but he didn't know what the Ring was, therefore he'd never seen himself as 'Fantastic Frodo'. Once he was told the power of the Ring, he owned it already, and knew that it didn't make him 'Fantastic Frodo'.
You don't ever have to have visions of yourself being lord and master. If the Ring crosses your path and you know what it is, than you'll start wondering: what couldn't I do with this thing? I think that is the power of the Ring, to make you start wondering and in this way creating envy and longing. What you think, whether you're thinking you'll be Samwise the Strong or Gollum the Great, it doesn't know and it doesn't care. You will be tempted!