Do one side at a time and support the length of the car with some 2x4s and jack stands...as many as you can until the frame rail is at least tacked in a dozen or so places.
When I had mine on it's side on the rotisserie, I supported the car in the center with a jack on the rocker panel. Once you have on side completed, the second side is not as critical because you have the support of the first sub frame connector. I don't envy you doing this with the car horizontal. It's a lot of welding, even from the side it was a big job. Use a good welder's apron, cap and gloves and wear a full face welding mask. Hot pieces of flux/metal is no fun on the skin.
Once you have the frame rail fabbed up and ready for welding onto the car, you can put the stands under that and rest the car on the frame rail.
If you want to talk about this when you're ready to go, PM and I'll give you my phone number.
Tim