I have figured out the mysteries of card slots in wallets! The higher-up slots have fabric "hammocks" to prevent the inserted card from going too far down the pocket and getting lost. The part of the slot that is seen is usually made from leather.
I am using a softer vinyl tarp for this project. The more layers of vinyl, the more the sewing machine tends to balk. At certain points it's two layers of nylon and two layers of vinyl to sew through. That also means that trying to encase a card slot module into a vinyl seam binding, fuggedaboutit! Too many layers. So I am using a glued-down strip of vinyl to hide the side seams.
Update: Tracy Murray gave me some valuable input on how to construct the slots to save some time. I don't have to have the nylon hammocks if I sew the slots down, starting from the back slot and working down to the front. Will try this technique on my next sample. Thanks, Tracy!