Thought I'd give some of my advice...
---If the only reason you have to keep the PSP is FF5, yeah I'd run through that game and set the PSP aside(or sell it). Two big omissions from the Vita's PSP Store are Crisis Core and Kingdom Hearts:BBS, though I think you would have played those already on your PSP if you had any interest in them.
---Here's a good list that will help you get an understanding of how much of the PSP's library is compatible with the Vita and what can only be transferred via PS3. Not sure how complete it is, since it hasn't been updated in awhile I think, it's the best one I've seen though.(NA store)
http://www.cheapassgamer.com/forums/showthread.php?t=316058
---And no I don't think you're crazy for wanting a Vita. I also was not a huge fan of the PSP, but am really enjoying the Vita. And if one of the big reasons you're wanting a Vita is for indies even better I think. As it seems the handheld is going to be great for indie games.
I have two little ones at home and it's become very hard to game on my PS3 nowadays so all those cross buy titles are getting the most game time on my Vita. They feel better on the Vita anyways.