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5 2R1A Push Fold spot and Theory Question

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5 2R1A Push Fold spot and Theory Question

Blinds: t10,000/t20,000 (8 Players) MP: 284,858
MP+1: 252,729 (Hero)
CO: 446,424
BN: 270,681
SB: 836,423
BB: 329,400
UTG: 681,792
UTG+1: 405,531
Last 16 of tournament and we are 13 out of 16. BB has been three betting quite aggressively but nobody else has done anything out of line.
Preflop (30,000) Hero is MP+1 with J Q
3 folds, Hero raises to 250,229 and is all in, CO folds, BN raises to 268,181 and is all in, 2 folds
So its a reasonably straight forward spot but I had a couple of thoughts that I hope someone can help with. I have run the above hand through ICMizer and the shove is +CEV but we only make around 3500 chips on average. Should we be looking to take any edge we can with only 12bb's or is there a threshold figure that we should be looking for. For example should we wait to make a shove that profits more than 0.5bb or 1bb or even higher.

I understand that r/f is also an option here but i chose not to because of the player in the BB who was playing back quite regularly. Overall is a shove in this spot too high risk or do we just have to push any sort of edge here?
Flop (568,410) T 8 T
Turn (568,410) T 8 T 7
River (568,410) T 8 T 7 8

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