I was typing as you posted results. I’m still betting $350. Hoping to get raised by a weaker boat and called by straights and flushes.
This was precisely what I would have done 95% of the time, and perhaps in hindsight still should have done here as well.
However, for better or worse I was watching him very closely as the river was put out. I was nearly 100% sure he liked the river, and that was before I even knew what the river was.
At this point I'm almost 100% sure he has a smaller boat (yay!) or quads (boo!). However, I'm not concerned about the quads in the context of determining my bet size because I am both 100% betting the river and 100% calling a shove. So if he has quads I'm getting stacked no matter what, no way around that.
So now in my mind I start to put less emphasis on making a value bet that a straight or flush can call, and more emphasis on getting as much money in as I feel his smaller boat can call. I decide that he's not folding a boat to a shove, and I end up deciding to do exactly that.
I announce all-in, and he jumps up and snap calls before I can even push a single chip forward. In that instant I thought he must have hit the quads (or the possible turned that the straight-flush) and I just calmly turned over my QQ fully expecting that I might have lost. Instead it was his excitement that was immediately tempered as he had neither quads nor the SF. He had TT and my queens full held.
The hand worked out for me (in this case), but I do question my decision to check the turn. The river shove was also questionable, and maybe in the end was likely moot in this case since he likely would have shoved anyway. But since the goal is to play these hand optimally, not based on the results, I feel there was room for improvement in the way I played this one.