Did you try to flush the heater core? The blend door has a pc of plastic that sometimes faulters.If you peel back the carpet and the padding then sneak a screwdriver in remove the motor.Before you do it put the heat at 12 o-clock then turn the key off.You can also open the glove box when the truck is up to temp and feel the heater core tubes one should be hot the other not as hot.
My guess is the heater core is shot.When you drop the dash to fix it do the ac too because that is going to leak soon anyway.
It is cool you want to jump in there.Just test everything before hand.I tryed all the easy things too.I am in the same boat you are.Spring time dash job for me.My heat is bad and my ac leaks.
The line going into my core wont even get hot, it gets warm, but not hot...?
I flushed it and all. Any other ideas?
I think theres lots of us having this problem with these trucks right now.