The Ring and the other races

[Boromir88]

Those affected by it envisioned themselves achieving greatness, or becoming mighty, or possessing/ruling something.

Not really. The Ring to Bilbo (as well as Smeagol) was more like a toy. Where they could play jokes, disappear, hide, they didn't take the ring in order to control other people, or achieve greatness, have dominion over everyone. They saw it as a valuable item, to play pranks on people, or to "cherish."

The Entwives to the Ents aren't just some "random turkey sandwhiches," it's creatures they've desired back now for a long time. That is a trait the ring can work with. It could offer the Ents dominion over everyone, and in return being reunited with the Entwives. The Entwives would be something the Ring would definately play with, in order to lure in the Ents.