I think the body will be more than 300 lbs, but it should be light enough for you and two buddies to heft into/onto the truck (though three buddies would be better). Attach 2x4s across the top of the bed somehow. Then you can attach bolt a ring on each body attachment point and use it to tie the body to the 2x4s. I think the front attachments are more solid than the rear so take that into account. Obviously, you don't want the body to move once it's attached to your truck.
Another thing you might consider is building something that attach to the truck bed and go into the section of the body where the 'T' section of the frame goes and bolt the body to that. It should be about 12" high. If you bring some wood, hammer, nails, saw, etc. You could make something similar for the rear. The attachment points seem to be a little less than 12" from the bottom of the body. The distance between the front and rear attachment points is about 8' (give or take up to 6").
Of course a flat bed of some kind would probably be easier. Are you sure you don't know anybody who races? They might lend/rent you a trailer that makes more sense.
Good luck!
