I had to perform a similar repair to my Invaders seat a few years ago. My upholstery skills suck. I just used a piece of vinyl to wrap around the front part of the seat, where the driver sits. I didn't even attempt to cover the compound curves of the stepped up back part of the seat. The good, old black duct tape had to do for a couple cracks in that area.
The front 2/3 of the seat actually turned out pretty decent, if I may say so.
I used a razor blade to cut up partway at the front corners of the vinyl, then wrapped the front of the seat kinda like wrapping a Christmas present. The places where I cut the new vinyl at the front corners overlapped, and once I had stapled the vinyl all around it didn't look half bad. I stopped the cuts at the front corners of the seat just before they would have become visible at the top of the seat.
I was ready to start an upholstery shop...
I don't know what to tell you about the back half of the seat...that will be a bear. Perhaps you could make the same kind of cuts in the vinyl at the back corners. Trouble is, they won't be hidden by the gas tank like the front corners are. But, it would be better than trying to "scrunch" everything up at the back corners.
Good Luck!