I’ve burped the system a bunch of times and have no air in the water pump, radiator or heater core. No sounds of any kind
Ok. That's good. A failing head gasket can sometimes simmer for years till it lets loose and screw up heating as well ...in some instances. You're not adding any coolant on a regular basis whatsoever, though...right? (spark plug color is all even?)
Just curious if the outside air/recirc damper closing all the way? If the outside air damper is broken or for whatever reason doesn't close ALL the way, there's not enough design-heat from the heater core to overcome all that cold outside air coming into the cabin. Unless it's 65 degrees outside. I know ...been through it. But you force-close a damaged outside air/recirc damper then suddenly it's toasty warm in the cabin like it should be.
I would read the factory service manual on the controls and heater box
thoroughly. There are troubleshooting steps in there ..beyond the scatter-gun things you get on the internet. At this point you haven't found the issue, you know enough how it all works ...you need to *expertise* yourself on how it EXACTLY operates to zero in on your problem using
a logical and organized troubleshooting approach. At least now you should know what works and what doesn't work inside your heater box. After all the time you've spent thus far, maybe investing time into reading it a long time ago would have gotten you there by now?? Not trying to be a jerk, just saying...you're close. But time to get serious now. Could be the controller, wiring, bad sensors???. Good luck. I'd like to hear what the final solution turned out to be.