Yes you will need to control the ambients it is hard to gain more than a couple of degrees and 70º is an average so that will go up and down now and again.
Yes a channel under the UTh will be fine. Make sure it is shallower than the probe by a touch you need the probe to contact the tape nut sit under it all together. I place a strip of alu. tape on the UTH where the probe is this will help even out the gaps in the tape and gives me more accuracy. Tape or glue the probe wire so that if it gets accidentally pulled it will stay in place. Make sure the bulge of the top is not too high. Most tubs have feet and the bulge should not contact the tub bottom this will prevent wear. Jim I do not know if you wear planning on a fail safe but a second grove on the top shelf maybe a good idea this is where I place my fail safe. The best use of a hydrofarms I don't like the fact the new heat tape gets hotter than flexwatt so I would highly recommend the failsafe. Even if you have a herpstats with relay. Everything can fail.