The way I made mine was: one sheet of plywood cut so it runs from the middle of the wheel wells forward. It isn't necessary to have it wider ahead of the wheel wells. Then another sheet cut to length to fill in to the end of the bed (or a little beyond is a good idea it seems to me), and also cut in width so it runs from the center to one side, and trimmed to the shape of the wheel well and tailgate. Notched around the tailgate it will stay in place and not leave out the back. A second sheet for the other side. Three sheets, plenty left over in offcuts but you need three sheets to get lengths and widths required.
It you wanted to limit to two sheets, you could rotate them as you say, I wouldn't worry at all about filling in a gap in the middle with a scrap. The one disadvantage with this is that plywood is stiffer and stronger the long direction, so the support out the back will be a bit less if turned sideways. On the other hand it will bridge the ridges in the bed better. On mine I actually did rotate the front piece to fill out ahead of the wheel wells, but I don't think that is necessary. I did it so that it could not slide sideways, but actually the wheel wells and railings I have on it do the job.
You could also use two sheets, cut one in half and have it forward, take the other half and offset it to the left, take half of a new sheet and offset it right as described above. You will not get an overhang, and will be left with 1/2 sheet of ply to spare.