$109 turbo: Shortstack bubble strategy

[xPeru]

This hand occurred last night and I keep thinking about it, so I would appreciate your views:

PokerStars No-Limit Hold'em Tourney, Big Blind is t1600 (8 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: 2+2 Forums)

saw flop|<font color="#C00000">saw showdown</font>

UTG (t1170)
UTG+1 (t9445)
MP1 (t2110)
MP2 (t17264)
<font color="#C00000">Hero (t4056)</font>
Button (t6930)
SB (t14920)
<font color="#C00000">BB (t4745)</font>

Preflop: Hero is CO with 4[img]/images/graemlins/spade.gif[/img], 4[img]/images/graemlins/club.gif[/img].
<font color="#666666">4 folds</font>, <font color="#CC3333">Hero raises to t3981</font>, <font color="#666666">2 folds</font>, BB calls t2381.

Flop: (t6887) A[img]/images/graemlins/diamond.gif[/img], 5[img]/images/graemlins/diamond.gif[/img], Q[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>

Turn: (t6887) 2[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(2 players)</font>

River: (t6887) T[img]/images/graemlins/club.gif[/img] <font color="#0000FF">(2 players)</font>

Final Pot: t6887

Results in white below: <font color="#FFFFFF">
BB has Ks 5c (one pair, fives).
Hero has 4s 4c (one pair, fours).
Outcome: BB wins t6887. </font>

Note this was a turbo, BB was Gboro780, not a donk. 31 players left, 27 get paid (1st level $177). Blinds will go up before they reach me again.

We're on the bubble, if I fold I think I'm 50/50 that 4 players will go out before the blinds hit me again. I know Gboro will call very light, as will the big stack immediately to my right. My problem is working out the $EV for this situation. Shoving here gives me a chance of making the $177 and provides opportunities for more $. But folding may well guarantee the $177. What range should I shove here? My feeling is that 44 is a shove and I'm being too nitty in questioning my play, but I've bubbled several recently shoving light on the bubble, and it's getting irritating. At lower buy-ins I'm shoving 44 without thought, but at this level, am I wrong?