Does your radiator have an in-tank cooler, in addition to the oil-to-air cooler? If not, than a new radiator with the in-tank cooler is nearly a must for that much weight.
Sadly, with the "gushing" symptom, you probably do need a new trans. Just be sure the root cooling cause is addressed before letting them install a new trans that may get cooked as well.
Also, there's sometimes a bypass valve on the transmission that fails and causes overheating. Do you have a trans temp gauge by chance? Are you able to read your actual coolant temps, via a device such as a ScanGuage?
