I think the key here is the blinds. My favoured move (depending on my read if their play and my idea of my own table image) would be a flat call. I want this to be a multi-way pot but I'm happy to spend 2000 chips if it encourages the BB move in and then the villain calls, I'd fold.
Assuming the SB folds or checks and the BB calls, I'd reassess depending on the flop, with position. Naturally, I'd call if the SB moved in and the either or both the BB and the villain called.
The danger of a push in the position IMHO is that either or both the blinds call giving the villain value to call which is not really what I want.