Homekit can't see or pair properly: Probably a corrupted database?

I recently tried to re-pair an ecobee3 thermostat with homekit. What happened was the ecobee said pairing was successfull while the iPhone said it failed. The ecobee did not appear in homekit, so I would think that meant it actually failed, but the ecobee had still configured itself as if it was connected, which doesn't impact its function other than enabling a 'disconnect from homekit' option in the reset menu. Whether or not I reset it, however, the thermostat now does *not* appear in any attempt to pair it in homekit (in the ecobee app or in the homekit app). I have verified that the ecobee does have a "Bonjour" beacon under "HAP" on the network, so it is broadcasting its existence on the network properly. on my iPhone (running iOS10), I deleted my homekit home (the most complete way to reset homekit in iOS10), and tried again, but it still didn't appear. I pulled my 4S from the closet, still running iOS9, and it did see the thermostat for pairing. Upon attempting with that, it again succeeded on the thermostat and failed on the phone. I've tried a full reset on my thermostat as well, and it still doesn't properly appear on my iOS10 phone, nor does it properly pair with homekit if I manage to see it in iOS9.

I'm fairly certain this means there is some stub in my homekit database that I can't remove, since homekit doesn't say the device is paired. This really does mean that, even though I've tried resetting both homekit and my thermostat, something has not been properly cleared. At this point, since I've reset the thermostat as much as I absolutely can, I think the very last thing I can try is to reset homekit on my iOS9 phone, and try again, hoping that the iOS9 reset doesn't just delete the home, but completely reformats the homekit database to remove the corruption I suspect is there.