Hero should
fold.
In this situation, considering the stack sizes, my main objective would be to eliminate BTN from the tournament. I would not want to risk tournament death here by going all-in against the big stack.
And that will be the situation if BB calls.
Meanwhile, BB (who would like to see Hero knocked out), if holding a decent hand, will be very tempted to call.
And BTN should be absolutely delighted at your shove! (If BB calls and scoops Hero, then BTN moves into second place). Sometimes the worst move is the move an opponent would be delighted to see.
In Hero's shoes I'd much rather wait to make a move until the very next hand, when BTN will be posting the big blind. And then if either Hero or BB raises BTN's blind, BTN will be on the spot.
I think this is a fold for Hero, even though he's probably ahead of BB. I wouldn't want to risk getting knocked out when BTN is this close to saying sayonara.
Buzz