I am beginning to suspect the secondary water pump which I replaced only 1 year ago, as the symptoms seem to match. If I rev the engine so that the primary water pump pushes harder then the heater core temperature rises and the IHKA can do its job of pushing warm air into the cabin.

The secondary water pump is buzzing like it is working, but perhaps the impeller is broken.

I hope to be able to take it out and bench test it sometime this week.