Southwest does go from Harlengen (HRL) to Dallas (DAL) but not to Dallas/Fort Worth (DFW). Even so, the round trip lowest price is still $220. And checking flight times, I would have of time to develop hemorrhoids sitting on my bum. For some reason, I cannot find the logic of going 500 miles north when I want to go 1200 miles south.
I too look for cheap ways to travel to Belize. (Not quite as studious about it as you however) A few years back, I believe it was 2008 or 9. I found my cheapest flight to Belize had us leaving Denver on Alaska Air to Seattle then after a three hour layover we were off to Atlanta another layover of nearly 3 hours. Finally we got to Belize City and took Tropic Air to A.C. We saved a few bucks (not worth it) but I always laugh that I left on Alaska Air and arrived on Tropic Air.