I am defiantly not using a slingshot. I'm also not going pneumatic, because I'd get pricy and we have a budget. I have a prototype hamp design im testing at the moment. If small scale works well, I'll make a full scale one.
I would be very surprised if this works well. HAMPs work despite their lack of stored energy because nerf projectiles aren't particularly energetic. Although scaling up the PT diameter would allow you to maintain the leverage ratio needed for a high exit velocity per plunger velocity, anyone who's strong enough to fire it 30 feet could probably throw it 60 feet. You lose lots of energy in leaks, friction, and most of all the stop at the end of travel.
Really, unless you're going with a giant air tank or CO2, a slingshot is your best bet. If that lacks in "cool" factor, you could compensate by making the slingshot a pseudo crossbow with a gravity feed system.