I live in the deep South, also. You're right, the heat and humidity are brutal. It's tough even if you already have an aerobic base, let alone if you're just starting out.
Things you can do:
Run at sunrise when the heat is at it's low (sunset is still very hot)
Allow yourself to go very slow, even taking walking breaks, if needed
Stash a drink bottle somewhere to hydrate during your runs (I put a bottle in my mailbox and do multiple loops, stop & hydrate)
Do more frequent, but shorter runs, to keep mileage same
Most of all, realize that you are gaining fitness (your heart rates prove it) and that if you keep it up, come late Sept or October, you're going to feel like a million bucks when the temp and humidity drops and be able to run faster, easier, long, with less effort.
Just hang on, you're not alone; we're all hating the summer-sufferfest. Just a bit longer and we're through it.