Ive never heard of plastic wrap but ive used tin foil and duct tape over the screen lid to hold humidity in and it worked pretty well, like you said make sure you include open spaces for air flow
As for the thermostat, just place the probe between the bottom of the tank and the UTH. The UTH should have a sticky adhesive on one side of it so no need to tape it down. Just make sure the UTH is stuck firmly to the glass and you should be fine. Also, make sure you have a temp gun to regulate the temps dont just trust what the thermostat says. I run all my set ups like that
I unfortunately have never put plants inside my enclosure so i cant offer much advise on that