Got no heat, flushed the heater core with a garden hose and a little bit of crud came out, and water flows thru super freely in both directions.

I have bled the air from the coolant lines several times and am positive there is no more air in there.

Engine heats up at normal rate to normal mid-scale temperature on the gauge, both input and output heater hoses to the core are equally hot.

I can see one of the blend doors moving (I think it's the blue arm) when selecting high vs low temps on the HVAC console, I couldn't see the other arm, I need to get an inspection mirror and a brighter flashlight to see both.

At low fan speeds, I get slightly lukewarm air at best from the vents. At high fan speed, it's just cold as the ambient air.

Is it possible for the heater core to have failed in such a mode that it's clogged, but somehow water is freely bypassing from the input to the output side within the end-cap and none going thru the tubes?

 

Could have scale built up in the inside of the heater core tubes, that is allowing water to flow thru but not transfer much heat to the fins of the heater, which is where the air passing over the core picks up the heat. Fill the core with some hot water mixed with some of the citris scale remover of your choice, let it sit for a while then flush it out again. See if you get any more junk out of the core.