actually that was a good thing that you inadvertently modulated the hose psi into the heater core cuz it ain't meant for anywhere near 60 psi. it may or may not handle 60 but it dont take that to clean it out. I'm thinking from your descrip that the core is flowing well enough (especially with the backflush) & that the prob (the heater core heat output) is elsewhere.
I've always used compressed air to blow them out and have never had one leak after. I'd change the core if you don't get heat after blowing out and also check the blend door while you have the box out.
