But more seriously, yeah, that core isn't flowing properly. Using 20psi of compressed air isn't going to tell you much about flow without a manometer at the inlet. I had a bad core that seemed to flow 'pretty good' with a garden hose but NEVER got hot. Finally had it cleaned out and fixed proper and it worked! Turns out it's tough to gauge things by touch/feel/eyeballs - a simple pressure gauge (manometer style) at the inlet would have told me a lot more than just staring at a stream of water...
Testing the core outside the dash is a good idea though. I'd swap it at the autozone for another and see if the next one is better. If not, it might be a case of 'consolidation' where a part number that isn't suited for your application has been substituted in order to reduce the # of core part numbers at the supplier - sometimes it works out in their favor - sometimes you get a piss poor substitution. It sucks, but that's just how it goes sometimes.
I also wouldn't rule out air in the core. Make sure it's at a low point of the system when refilling and that the stat opens a few times to clear the air out of the system prior to making any judgments.