Try your local Greyhound. they take a bit longer, but I had a Trunk lid and a front cowl complete with A pillars shipped to me that way. The trunk lid for a 66 dart cost 65.00@62lbs to ship 3 years ago. The cowl was last year at 75.00@90lbs. The shipping was slow took 2 1/2 weeks to get to me due to them being such a big item and it's shipped by space being available. They both came in undamaged and wayyyy cheaper than UPS or Fedex, USPS wouldn't touch them due to size. Package them well and the seats should be no problem since they are a lot smaller than the trunk lid.
I'd do each seat bottom separately and both seat tops together. with all hardware in the seat tracks package
I'd use 3/8 plywood "+1 to3 inches per side for safety "on the bottom and top with 1x2 runners to locate the seat tops (couple of layers of 2" eggcrate foam to stop the plywood from ruining the back panels) put holes in the bottom piece of plywood and mount your seats to that for stability. Wrap(a lot) in shrink wrap and done deal.
or you could do the same thing using 2 or 3 layers of box cardboard and make it lighter and wrap around the sides to protect the vinyl better.