As for removing the UTH, it can be done. I've moved them before. It just takes patience, go nice and slow and try not to bend the mat. Bending the mat can break a coil, ruining the UTH. They also need to be taped onto the new enclosure because they won't stick as well.
On the t-stat topic, if stay away from Zilla and ZooMed. I haven't made the jump to HerpStat YET, but will be in a few months when I start my enclosure upgrades. I currently use Jumpstart and Big Apple and am satisfied with them, but ultimately want to upgrade when I've saved enough cash.