How long has it been since the plug you had heating problems was disconnected.
If a plug is left for a long time corrosion will build up and cause a high resistance connection.
I have a Hughes Autoformer that was permanently mounted in my trailer. I had used the plug connectors and they were never disconnected as I always used the Autoformer. After about 5 years I discovered the same heating and melting problem you described.
I removed the plugs and made a permanent connection with wire crimps which I soldered after crimping. This required opening the case of the Autoformer which I did not mind as the Autoformer was way out of warranty.
If you do not want to wire direct I would recommend disconnecting and reconnecting the plugs after each trip. This will break the corrosion that forms.