Your MO combined with your inexperience with towing is why you now need a bigger tow vehicle. There were many Forum members trying to explain payload ratings and how they effect towing before you bought the Toyota. Most advised some cushion or headroom between rated weights and the actual towed weights. I think you are now finding out why that is advised.
My suggestion is to buy a large SUV or if you have plans to get a bigger TT in the future, buy a bigger truck. 3/4 ton or even 1 ton trucks are where you should be looking. If driving a big truck for shopping is a concern, either keep the Toyota or buy a smaller vehicle in addition.