Check raising the flop is a great line to take; bad luck it checked around.
Snap call the river raise.

I think leading on flop is bad compared to for going c/r because fairly likely no one going to raise after you lead which keep the pot small and maybe give good implied odds to hands like 56 and 9 10 and make them play their hands optimally. Going for c/r makes more sense since you have relative position wrt aggressor which makes fairly likely someone will bet and then you put more money in pot with best hand.
On river it is a bit weird spot. His value range is 22,77,AA, sometimes 46s. He could play 22/77 deceptively. He very very rarely play 96,23. If he is raising thinner then some aces up also add in his range but that is a bit less likely with pot raise. Since you are 300bb deep 3 betting shove will be -EV against that range. With 200 bb shoving is better than calling. Here it is a call at least.

I prefer a flop lead in a multiway pot where PRF is less likely to c bet.

Turn is actually not a terrible spot to go for a c/r as the A does hit villain a good amount.

Snapping river raise. Think raising is closer than folding. However, think we are too deep to reraise.

I think there are merits to both lines. Clearly our dream scenario is letting CO Cbet an overpair and have Bu or SB get nuts with something before it gets back to us. I think our decision boils down to our read of the CO and what his cbetting range is. The more likely i think a cbet from him is, the more i like a check. If you've observed him failing to cbet in multiway pots frequently....i like a lead.

As played i think it's an easy call on river, but im not loving it. If he has AA or 69, then so be it. There are too many Ax 2 pair hands, poorly played sets and air in his range for us to fold.

Lead flop. You dont want to give free cards here and small draws will be gunshy to bluff into so many ppl.