That's a hard one, but you'd think the refs would be a little flexible in their climatic resolution.
Seriously, I can't blame the refs for kicking it to the sideline as opposed to picking it up. I've had a player throw up on the field when coaching a game before and we tried to run everything to the opposite side of the field whenever we'd get back around that yard line later in the game.
I think the there are a couple of NFL refs that could pull off stating a call on this ... could bring Ed Hochuli out of retirement just for this. For the first incident of the season, maybe it's like a sideline warning, with a mic'd reading like, "Sideline warning. Frustrated fan with inadequate partner or inability to secure a partner. Next instance will result in 5 yard delay of game penalty against *insert team name here*." No pun intended on the insert. Immediately after the infraction announcement, the stadium announcer could announce that fans are requested not to throw foreign objects or marital aids on the field ... and that batteries ARE available at the concession stands in the lower concourse. Of course, it could just be one of the old standby calls with a little modification, "After the play, the fan in the stands was givin' him the business."