I wonder if you could register using all the plate numbers from a nearby car rental place, then try to rent the corresponding car if it gets chosen.

Rental cars actually add an interesting aspect to all of this: if you use a disposable (not also used to buy your ski pass) email address and the license plate of your rental car for a reservation, the resort will have no way to penalize you for being a no-show! Any attempt at collecting a fine, prohibiting future business, etc. would be against a useless email address and plate number that you don't reuse the next time you visit.

Also, once you've managed to get a reservation, the system allows you to modify the plate number on your reservation, presumably to allow for renting after reserving.

And you'll need to address this whichever approach you take. If you can't pin them down to an identity, you'll probably need to take a deposit.

Type many fake invalid license plates, and cancel them, freeing a spot at a time of your choice.

You don't need to cancel a reservation in order to convert it from a bogus plate number to your actual plate number. Changing your plate number is already permitted by the reservation system.