You got a little unlucky on the GMAT. I had the exact same Q/V split and got a 750. That said, higher is always better, but I don't think that a small bump will help much. So, only do it if you are confident you can increase the score without much risk and effort.
I don't see any reason to concentrate outside of the top 50. I would apply broadly, but could easily see top 20 programs taking you. My PhD school was top 20 and has taken several people over 35 since I started there. If anything stands out to you as a place that matches your research interests, I would apply there. Otherwise, I would concentrate on schools that have a solid financial/archival ranking from BYU's website.
I don't think full funding will make a huge difference. PhD students are a cost, but the biggest cost of them is faculty time, not the stipend/tuition. Of course, it couldn't hurt if that is something that you could secure.
What rank of school are you currently TAing for? Are your letter writers active researchers?