Remove blower motor and squirrel-cage, look in the air box with flashlight and mirror. The heater core is "right there".
What debris gets through the heater core then ends up stuck in the A/C evaporator.
Compressed air backwards through the air box helps a lot, but some of it I just had to pick out by hand. I have seen but never used a foaming aerosol cleaner specially-made for HVAC heat exchangers. They sell it by the gallon and by the aerosol can at the local home-improvement store. The gallon jug gets mixed with water and then sprayed on with a pump sprayer. The aerosol works just like any other aerosol can, push the button and "instant foam". This stuff is "supposed" to be really good at cleaning dust, dirt, grease etc; but I don't imagine it'll work worth a crap on pine needles and cottonwood fluff.
I can imagine a situation where the only way to truly fix the blockage is to replace the heater core and/or the evap.