I don't know how close they check either, but I'd be apt to just call the rental car company directly and ask if you need one card or three to legitimately use the coupons you have with the reservations you've made.
But I've always been able to get a better deal with combining contract IDs and coupons than I ever do with just the Entertainment discounts, so maybe closer to your dates you can get better rates that way and the card problem will be moot.