I have a similar issue - and I've replaced the blend door actuator already - have not flushed the heater core (nor replaced it), but I did check for flow to and from the Heater Core in the engine compartment - yes that was a mess....

Similar truck - 2000 LT with teh auto climate controls - what else would you guys check? I've been driving with no heat in WI winters for 3 years running now...my old bones are tired of it tho and I'd like to get this fixed before it gets really cold out, also I did burp the beast with it on ramps while checking the flow to/from the heater core

Any additional diagnostic check ideas would be welcome...