Less effort needed than that - charge $1 for a reservation. Just enough to be a valid purchase.

Ask them to check out with the same credit card at the end of their meal.

Blacklist any card used for a reservation consistently not matched. Cancel all their RSVPs.

We don't care about the odd reservation where someone books and someone else pays - that's rare and individual people don't book that many reservations. Worst case they call support and you set a note to not apply the rule to them.

This means scalpers now need to rotate cards. That sucks and is going to hit other limitations.