O.K. you got me confused here. You've carpeted the panels and stapled on the back side and now you want to install them by screwing them to stringers. If that's correct then I don't understand the worry about the staples unless you didn't use monel or stainless staples in which case they will rust out in a year.
OK. Just seal them up with a little 3M 5200 and you'll be fine. I just put a little on the screw threads so as not to make a mess, it doesn't take much to do the job.
Think about self adhesive velcro to hold carpet to wood deck. screw the wood down then velcro the carpet to it. no staples no screws thru the carpet. Change it any time you like without lifting the deck.
Only problem with that is that now you have to have all of the carpet edges bound or it will unravel on you. We do a similar thing with our Lino decks except we use snaps to hold the carpets down.
