Keeping it fresh and repeatable is a seperate issue to whether it's worth the upcharge, which I believe dungeons are.
I'd manage it as so, usual cost £10-15 (end price, assuming you've used a 241 or whatever)
If you have a park ticket it's an upcharge of £5 (or whatever is normal at Warwick ect.)
Open the dungeon to all, with an emphasis on outside of park hours. (Not just park guests)
Offer discounts on food/beverage in the tavern to those who actually went through the dungeon (to encourage people to go in).
In order to reduce operational costs reduce the number of slots available, giving you the option to shift staff around. (Actors, in park during park hours that the dungeon isn't busy, madness!)
Somehow Merlin seem to keep the dungeons busy, and while I appreciate that passing traffic is very valuable, they've got a bunch of people sat in hotel rooms with basically nothing to do... People might say why not.
Advertise it as something to do to avoid rush hour traffic too.