After moving my hub right next to my thermostat and excluding and pairing AGAIN, things are now working. Thanks to some more help from @RBoy, we figured out that my Z-Wave Raw Description in SmartThings was showing up weird. I was getting:
0 0x0806 0 0 0 f 0x20 0x81 0x87 0x72 0x31 0x40 0x42 0x44 0x45 0x43 0x86 0x70 0x80 0x85 0x60
But it should have been:
zw:L type:0806 mfr:0098 prod:6501 model:000B ver:9.00 zwv:3.28 lib:03 cc:20,81,87,72,31,40,42,44,45,43,86,70,80,85,60 epc:2 ep:['0806 31,85']
At this point, I’m assuming that the previous Raw Description was due to low signal, but apparently still strong enough to pair? After getting that straightened out, I was able to put my hub back and control my thermostat using this DTH again.