Hi Scott,
I have a 58 and 60 Bugeye. All my seat bottoms look like the pic you posted on the lawn, but they have a metal plate with holes welded to the bottom portion. I am guessing this gives the seat a little more flexibility? It probably doesn't help much now, but I posted a picture of one of my seat backs in the area you needed yesterday too. I bought a book that stated how easy it was to cover these seats, but I found it anything but easy. The brazing, blasting, and painting weren't too bad, but trying to line up the sewing lines in the back and bottom was a royal pain. I also had a heck of a time stretching the cover over the seat base parts. I ended up heating up my bathroom to make it easier do the bases. I have see many Bugeyes where the lines are crooked or don't match up and it is very noticeable. Many times these were done by "professionals". You put so much work into your car. I just wouldn't rush the seats at this point. Just my two cents.
Kevin