So, I logged in to the website and looked at an existing reservation - the credit card information session does show the old expiration date, I attempted to update the expiration date, I then checked the reservation again, and the old expiration date still shows. At this point, I don't think the expiration date actually matters, as the expiration date is correct in my profile, the card number is the same, and my letter from the credit card company stated that "expiration date and CID should not be updated for online payments or renewals unless asked for by the merchant."

I'll be keeping my 88 reservations as is because frankly, I think the card will still work, and I very rarely get non-physical credit card charges anyway. I won't be switching each reservation to another card and then back to the new card - too much work.