Anyone wanna tell me what the heck is going on here?

Never seen it before? I have seen this on almost every car I have owned. Worst was an 82 Chevy S-10 I bought new. Green fluid on the passenger floor 2 yrs later. Like others, I bought a new heater core for my 65 Dart (non-AC) for ~$35 from rockauto I recall.

I agree on checking the cowl drains since they can easily clog. There are little triangular openings at the cowl sides, simple folds in the sheetmetal. You can get at them thru the door jambs, or really see them if you unbolt the inner fender. A rusted out cowl is a serious problem and very hard to fix, so I painted the insides of mine using a foam brush on an extender thru the openings in the engine bay and up thru the air box holes.