Here is how the story ended: While the core was out, I back flashed it with tap water and blew throw it. Some dirt came out, not too much, but noticeable amount. Looks like the Preston cleaners have not done a good job here.
I've put everything back together and so far I think my problem is kind of solved. I realize that back flashing the core has nothing to do with the air flow strength, but it seems to be back to normal. Why? I don't know. The air temp though got hotter as well as the core output pipe. May be that gives a feeling of a better air flow.
The good thing is that now I'm a heater core replacement expert! ))
