Ah, okay, I just tried again and I remember the problem (since it's still happening): with Chrome, I can't launch the hangout at all. It opens to Google Hangouts, but I am unable to invite people OR start the hangout without inviting anybody, so it pretty much dies at the "invite some friends" stage (in fact, with Chrome, I didn't get the "type some names" box). I wrote off using Hangouts the first time that happened - if it didn't work with their own browser, I'm not going to chase down a solution.
However, it did work just now with Firefox - I was able to launch a hangout to see what Roll20 looked like in that interface, and it operates glitch-free. However, I don't think it solves my particular screen space issues - with the app jammed into the 4-5 inches in the middle of the screen, I think it's basically six of one, half-dozen of the other as far as screen space goes.
In any case, nobody in either of my gaming groups uses Google+, so writing off hangouts was not a big loss. I'd have nobody to play with anyway. :)