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I think the preflop minraise is AA or AK enough that you can safely push. Considering that donks love the minraise and you had an inkling that he was one, it is a good push in my book.

I don't see JT minraising often although perhaps 99 / KK / QQ is just as likely as AA / AK. I would go with what is a positive EV push IMO, taking into account bluffs and other hands such as Axs / ATo / KQ / JJ / TT.

One thing that might put me off is that a large overbet on a wet board like this is sometimes a set that really doesn't want to be drawn out on. But in the end I think it's just too hard to fold the 2 pair unless your roll is low and you're worried about variance.