Awkwardness. 125 effective, JJ 3bet SB vs. HJ. Low card board, do we call river shove?

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Awkwardness. 125 effective, JJ 3bet SB vs. HJ. Low card board, do we call river shove?

Blinds: $1.00/$2.00 (9 Players) MP+1: $186.00
MP+2: $245.70
CO: $195.35
BN: $26.17
SB: $529.60 (Hero)
BB: $202.00
UTG: $205.45
UTG+1: $382.80
MP: $178.00
Preflop ($3.00) Hero is SB with J J
4 folds, MP+2 raises to $5.00, CO calls $5.00, BN folds, Hero raises to $25.00, BB folds, MP+2 calls $20.00, CO folds
Flop ($57.00) 3 2 3
Hero bets $22.00, MP+2 calls $22.00
Turn ($101.00) 3 2 3 6
Hero bets $60.00, MP+2 calls $60.00
River ($221.00) 3 2 3 6 6
Hero checks, MP+2 bets $138.70 and is all in

No reads on V.

First off, should we be shoving river? As played...

On one hand, given this is a squeeze preflop, his range should be narrower than a typical SB vs. HJ 3bet spot. I would expect his pairs < JJ to check back river and maybe even some Ax spades checking back for showdown value. We are blocking some of V's other missed flush draws. And given my pool is generally softer than others, I wouldn't expect a well balance value/bluff range on this river. That leans me to a fold...

On the other hand, from a MDF perspective, JJ should definitely qualify as the higher part of our b/b/x line here and thus a call.

Bottom line, this spot just sucks :(

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