looks like you are doing the right thing, but man.... that kind of sing generally means bad fins on the heather core
I've had couple of vehicles with that problem. can you smell the coolant inside? if not it could also be the small hose that evacuate the moisture of the AC through the firewall right by the heater core, I fix mine last weekend as I was seeing a bit of water on my slush mats, took me like 20 min and I didnt post it because I didnt think it wasn't a big deal. Now, if it smeels coolant inside...... well, good luck.