Easy to get rid of it, you'd just follow the lead of Vegas and YouTubers. Once you have a ticket, you pay extra for a ticket to a meet and greet, where you would spell out what they would get, who would appear (without guarantees), and then that extra $$$ either goes to BC/EFA or as overtime to the actors, divided up by their meet and greet attendance. You could also pre-order a cast-signed Playbill, window card, etc., in advance, and just pick it up at the merch booth.
Once it is formal, the cast would feel no obligation to stagedoor, since they just met audience members before coming out onto the sidewalk.