I always figured a lottery would work best.

Accept reservations (maybe with a token deposit or a card authorization to discourage making too many claims) for a week. Then at the end, draw winners for each block of seats; if they don't claim them in 48 hours, draw from remaining reservations. Repeat a fixed number of times and then scrum-sale anything that didn't go through.

There's no more risk of "the website crashed for everyone but scalpers" if you have a full week to place your request.