No solenoid drivers are available to power it. You'd have to piggyback off another device or wire it up fully mechanical like an EM sling.

Correct, System 1 slings are directly powered, no boards involved.

I've often wondered about doing a similar mod to my Genie, which has the same issue: right sling doesn't have a kicker. But I'm not quite willing to cut a hole in my playfield to find out if it plays better

Modding close encounters would be harder though, since you'll need to cut a slot for the kicker, and holes for the switches to sense when the ball has been hit, since it doesn't seem to have any switch?

I'd be concerned whether you can actually fit a sliingshot and 1-2 switches in on this game, considering how small the rubber is. I can't really think of any games with bumpers that small that have slingshots. (Joker Poker, Count Down, and Volley come to mind as other games with small bumpers like this). Some other gottliebs with small bumpers like Gladiators and Bone Busters use kicking targets instead of slingshots.

Might want to start by getting a spare bit of plywood, and spacing out the same posts, and doing some test cuts to see if you can fit everything in and it still works well.

I always found Bone Buster’s kickers really neat. My vote is add the solenoid in, provided you have space.

It's your pin. Whatever makes it more fun for you is the right thing to do.