When I worked in resorts half of the roles you could train in outside of your basic front desk position were considered "advanced" and had a premium attached to them. They were much more demanding computer and phone based back of house positions that a lot of people didn't want to do so once you were trained in them you did them almost exclusively. It was an easy way to get an almost permanent pay bump without having to work much overtime and when you DID work overtime (which wasn't hard to get) it was even nicer.
Honestly OT is really only hard to get in certain lines of business. A lot of food positions, pretty much all merchandise and many lodging positions are interchangeable no matter where you work so there's always open shifts and people can fill them easily. Sometimes the company puts limits on who can pick them up so people who would get straight time have the opportunity first but will open it up to OT if the shifts aren't getting filled.
I feel like the people who struggle with OT are things that require specific training like Attractions and certain entertainment roles. If you're not trained in that specific area, you can't pick it up. Even if attractions share similar positions (like a person at the entrance to check height requirement for example), if you're not trained on that attraction, you can't pick it up.
Operations has a lot of untrained roles with open OT shifts, usually crowd control. Certain attractions have untrained positions available - generally the greeter position, as you mentioned or tending to wheelchairs/strollers. You don't even need to be statused in attractions for many of these shifts. People pick up from all sorts of other departments.