Reason to shove this hand would be that even the BB wouldn't be happy calling off half his stack on the bubble without strong hand, and if we don't shove this hand, the big stack will be in the BB next hand and makes it even harder for us to steal.

We're obviously in dire situation; should we really just fold this and let CO double up or bust before getting (our then extremely short stack) in?

[converted_hand][hand_history]Poker Stars, $3.16 Buy-in (150/300 blinds, 25 ante) No Limit Hold'em Tournament, 5 Players
Poker Tools Powered By Holdem Manager - The Ultimate Poker Software Suite. View Hand #37260247

BB: 3,969 (13.2 bb)
MP: 17,831 (59.4 bb)
CO: 1,111 (3.7 bb)
Hero (BTN): 1,770 (5.9 bb)
SB: 2,319 (7.7 bb)

Preflop: Hero is BTN with T 4
2 folds, Hero ???

I agree we should look for spots to gii soon.
But T4o is just too meh here to do this. And yes 6bb is short, but I would just be patient and look for a hand with more equity when called. Wouldn't be surprised either if any other stacks were totally unaware of ICM and could make huge ICM mistakes there.

Easy fold.

You can't shove this. Reason the charts exist is because of the equity you have against the top 10% ( or whatever)of hands that do call.