The tried and tested system in the past ,when they have been short, has been to be interviewed/accepted, and then when the offer comes, state plainly that you will only accept if given XYZ base. It worked in the past when they were short, I cannot see them sacrificing their short term needs merely to satisfy the long-term contentment of any incumbent (un)happy bunnies.
Not pretty/fair but hey, you are joining them, may as well get used to it . . .your turn will come soon enough to be on the receiving end.
In my humble opinion of course.