I found just the solution for 12 BB, but it should be very similar to ~ 13 BB spot.
So as Hokie said, we should be checking these weak FDs. Because we have a lot of pair+FD type of hand, that prefer betting here and we are calling a jam with 90 % of them when villain shoves.
Here's the strategy for FDs:
Here's the overall strategy:
It's surprising, that we are supposed to be betting here with 61 % frequency.
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As played, I'd probably bet the river small.