Allocation codes might be your best fix for this.
That was going to be my suggestion as well. I know custom sites can sell hold codes online. If TNEW can do it out of the box, I forget how.
When we do something like this with, say, ASL, we do a Mode of Sale shift with an Allocation tied to that MOS. That helps us ensure that only people that need the service (hopefully) buy those tickets. We also put specific messaging on that specific performance in TNEW with a link to the same show with the code embedded and removing any prior promo code to avoid that roadblock.