Where did all this water come from?

Ignore James. ASE tech,my @ss. It would be leaking COOLANT into the car if the heater core was bad. What you have is a clogged drain for the AC unit. The condensation that would normally drain outside the car and drip on the ground now has nowhere to go. So it runs down inside the car. Find the drain and remove the gunk that's blocking it,replace the drain hose and crank up the air.