Sounds right to me! Tubular construction radiators were designed to run a high pressure cap, which is what you've got now. It gives you a lot more safety factor in case you hit a slow traffic jam, have air conditioning, or run a trans cooler, which it sounds like you do. An auto trans can put a LOT of heat load into a radiator, ditto with air conditioning because all the heat from the condenser gets dumped right back onto the radiator.
Jerry