Not a clogged heater core but rather a blocked evap core. A certain percentage of air passes through the heater core depending on the temp select setting. 0% for full cold to 100% for full hot. All of the air passes through the evap core all of the time though. You can inspect for a blocked evap core by removing the blower motor resistor assembly under the hood. Here'* what you may find:
Pine needles, leaves, etc
These are not the only causes for restricted air flow, just three that I've come across when I had a camera handy. If you are confident that your cleaning efforts described above thoroughly cleaned the evap core then I can only think of one other problem. You have a moderate to large crack, hole or breach of the climate control "box" and air volume is being lost dehind the dash. You can inspect the heater core door first. Get a hand up there and feel for blowing air where there shouldn't be any.