(unrelated - started an EV tree to see whether flop raise or flop flat is better... and wow that spins out of control fast - because of whale in hand, and guessing who wins when the extra diamond or board pair scares... etc - so in conclusion I will trust the pros like Ike/SABR/etc who advise flatting)

But on river shove Taox... I don't think a shove is getting called by less than a set,
(3) TT
(3) 77
(6) flushes we beat
(15) flushes we lose to - QdXd to 9dXd

... so a shove is -EV

However, smaller bets bring back in some two pair hands, so a small bet can be +EV. For instance, AT produces 9 combos itself. I say betting ~$300 as played OTT will get looked up as light as AT (or lighter)

Yeah like I think the NF or 2nd NF are probably leading the river, this hand was just tough for me to play in game. My heart started racing and I was having trouble thinking straight and I think I prefer betting the river.

That being said, I think 450 > shipping and I mean he has A7s in his range but I don't think he has AT in his range.

Also I'd say he has like 96dd in his range but not really 95dd thru 92dd and probably like J5dd+ and all QXdd.

I think I'm betting around 400-450 otr. I don't think a pot sized ship is a good plan. You need to size it smallish so that you can still get called and be good 50% of the time.