Do the math
I called Causeway and they try to rent out July weeks for $2470 with a 65%-35% split. Given that what would you ask on Redweek, Craigslist, TUG, etc.?
I'm not proposing that you have the resort rent it for you but ......
If Causeway can rent your July week for $2470 then your cut (in an ideal world) would be $1605.50. Fairly decent price after their cut.
The big question is 'WILL THEY?' Always the big question.
But back to your question. What should YOU ask for it?
I have no clue what the market will bear. The management can advertise that price and then offer a discount of, say, 25% off. SOP in the hotel/accommmodations industry. Every price quoted by management is a retail price, an 'I wish I could get this' price!
Just for your own information, you need to find out what their rental policy is. Do they allow you to 'take it back' after you've placed it with them? What happens if they say they have it rented when you call (because you have a renter) and then their renter changes his/her mind? Do they keep a deposit and share it with you or give it back to the renter within so many days of check-in?
If they have lots more inquiries than they have units available for that time of year, you could do very well by listing with them. However, except in unusual management circumstances, most resorts rental programs don't pay off very well for owners. Generally, the resort will rent their own inventory first. Often, it is an all or nothing proposition (and the 'all' might not be that much).
You could call the resort and act like you're a potential renter who wants to rent for that time. See what they have available. Ask what other types of units they have. Ask them if that is the best price (perhaps they offer a triple-A discount).
The one advantage the resort has over you is that they advertise ALL their units with their advertising dollars. You have a very specific time and unit size. I'd mention in any ad you do place that the resort would charge $2470 for the week.
My 'gut' feeling about what you should ask is 'about $1235' (half what the resort would charge). This is not a rule of thumb but a gut reaction to the price the resort would charge.
You might consider putting it into Donita's Dial an Exchange rental program. If it doesn't get rented by a certain day (30 days out I think) it automatically converts to a deposit for an exchange later. You should verify this with Dial an Exchange of course. I'm pretty sure they take a cut of the rental price but handle much of the 'paperwork' (notifying the resort, etc.). You should verify that with them too.
As always, just my three cents worth.