Spyders were no frills race cars. If you are attempting to build a true replica then no carper; only rubber floor mats in the foot wells. I had full carpeting in my Spyder and liked it. I also covered the rib in front of the seats. Without something there you will soon scrape off the paint getting in and out. Carpet covers a lot of sins.
Note the rubber floor mat on the drivers side. Carpet did not work well there and wore quickly.