Running A/C with extension cord into 20 amp outlet.

By that logic, is my 30 to 15 amp dogbone being overloaded also?

Maybe. We don't know what's inside it and can't judge if it gets hot or not.

If you had an inexpensive Kill-a-watt meter you could be seeing what is happening, electrically, along the chain of that circuit. The inrush current will be momentary and not measured but the load will be metered.

Yes, a 10 ga cord is better than a 12 ga cord but a good 12 ga cordset should handle the current at those distances.