This is a fairly clear fold, you have to push through both of the big stacks, and everyone (especially the SB) has to be much tighter than I think they're likely to be (on the order of 66+, ATs+) for this to have a chance of being +$EV.

Moreover, even if they are that tight, BB should be calling a wide range here, and he doesn't have to be calling all that much for this to slip into negative territory.

Overall, you're likely better off looking for chances to attack the other middle stack (or even the #2 stack) when he's in the BB.