UTH heat tapes come in various widths, some cut to length, to customize whatever size (dimensions of enclosure) you're working with. Yes to install question for temp. probe (under PVC- between enclosure floor & heat tape.) Be patient- PVC is more insulating & will take a long time for heat to build up- test temps. for at least a week before snake moves in, & keep substrate shallow over the UTH. (substrate = insulation, lol- so many don't realize that)
Ambient temperature of "low 80's at the most" is the highest a corn snake should be- you'd be turning the heat OFF when it's about 80* as they won't use it anyway. They seem to prefer about 75* ambient, with an option at one end for nothing higher than low 80's-(85* max over UTH- & certainly not the whole enclosure)
Your low winter temp. is fine with UTH provided, but it's sounding like your mid-summer might get too hot for them, unless you take them to a cooler part of the home?
In the long run, 24" height is preferred, but you're correct that it's much harder to maintain the proper temperatures. If 24", you might want to use an external heat source from above (a light or CHE) to warm the upper part of the enclosure from the outside- or even a heat pad might help? Gets tricky (& dangerous) to put light/CHE inside, even with a cage to keep the snake from getting burned on it, since corn snakes are good climbers & metal mesh may prove dangerous. (I'm a glass tank fan myself- full disclosure.I keep mostly rat snakes & they do best IMO with good air-flow- not a PVC fan here, sorry.)