I think Southern Water might be a bit more amenable to helping out on a temporary basis given the circumstances.
Although the agreement with Sussex Uni is for 1100, I think there are probably more available on that site too. I suppose the council might consider some limited parking in Stanmer...
2100 according to a recent planning application. They are obliged to provide a minimum of 1500 and maximum of 3000 spaces.
So they could provide an additional 900 without falling foul of any planning conditions if they can find them. I know they have attempted to gain permission from Southern...