First off, keep at it, and stay away from spending money on a simple fix.
The tpm sensors are direct.
Here's an idea, I haven't had my spare tire mounted on my rig for over 3 years and I never had the need for it!(It still has the original unused tire from 2007)
Take your spare off, set your pressures to 38psi, then drive.
If that doesn't work, you have a defective sensor, NOT a bcm fault!

 

I realize the BCM can only read 4 TPMS. You need to make sure that you are communicating through with the 4 on the ground and not the spare. Take it to a tire shop and have them program all 4 tires on the ground. For some reason your rig may be communicating with the spare you said has a TPM on it.

 

Dealership experience was a waste of time.....since they only signed me up for a half hour of diag time, the tech didn't get into it very far, and gave me bull-s information to boot. Unbelievable, I know more what's going on with it than he does. He said his Tech 2 scanner showed the bcm was only seeing 17 lbs of air in the left front, and suggested I change it then relearn them again. My tpms tool showed them all working perfectly but I changed it anyway. Naturally, it didn't fix it. Then, using my friends Snap-on diag tool, it actually shows the bcm only reading 17 lbs in the right front. So the tech probably f'd up and told me the wrong front tire. Waste of time and money. Paying them to give me bad information and then spending more money on un-nessasary parts. Also, they're poo pooing my aftermarket sensors since they ain't factory ones. The bcm won't even go into the learn phase properly, that's the tell tell sign right there, the horn beeps, but the light on the dash is supposed to flash too, and it doesn't. I read somewhere, that other GM vehicles of this era, the serial bus on the bcm can go to sleep, and it won't wake up to be able to learn or relearn the sensors. So, the dealer has to reflash the bcm to wake it up. I think something like that is going on. I'm not f-ing changing all the sensors to factory ones, just to have them tell me it still won't learn them. If the light on the dash would start flashing like its supposed to, I would change the sensors. But I'm going to get a new bcm and see if that fixes it. Or find a dealer that will reflash it to wake it up.