Thanks for all the sage advice. As usual, I only have to ask to receive instant help from the group.
The 2003 Chevy ZR71 4 x 4 extended cab 1500 series truck I was looking at is rated with 8,800lbs. capacity. It has a 5.3 liter gas engine. While it will be used a dozen or more times a year to tow the race car the rest of the year it will be a semi-daily driver, so I was trying to find a vehicle that less like a semi-truck and more like a car for off season excursions. That's also the reason for the backseat.
The trailer is 3,220lbs. Add a 2,650lb car plus 1,000 lbs. of tires, gas, canopy etc. and it will be over 7,000lbs. That seems safely under the 8,800lb limit. I have load distribution bars on the trailer and new electric brakes. It sounds like the engine can tow it but stability in the wind could be an issue. How about over-heating of the engine, transmission, differential? Does the factory towing package address these areas?
I think I'll find a 2500 series and see what is it like to drive.