I think in all honesty if you are not calling in this spot you shouldn't be playing this deep.....
500bb is alot to lose in one hand, but if your playing 250bb this isn't even a discussion, it's a slam dunk high five call.... the maths really doesn't change that much by changing 250 to 500 bb so you should be loving life, but no one wants to lose 500bb in one hand which is the only reason you would fold here...
I would expect villan to show up with a set or top two here pretty often

It's a call on paper given you likely have 50% even if holding the Ah (less FDs for V ldo better for you than having the backdoor equity)
If you have a strict risk-tolerance policy then it's ok to fold considering you may not look to be utilizing 500bb for EV near just a fraction of a single BI.

If you estimate he has any OP hands in range at any frequency then snap.

comeon these arent actual 500bb hands. these are super typical home game stacks where stacks and buyins and raises are inflated. OP even says it plays more like 2/5 making it 200bb and a super easy stack off except vs very specific reads and a very tight villain.

I really question if some of you that post in this forum have ever even played live before.

Answering your questions.

I don't think he's raising 62 ever. He certainly could raise 76s though not all the time. 76o is closer.

I don't recall any huge overbets from him post flop. He generally plays his value hands strong and is not trappy.

If this isn't a 4+ BI shove (guess it isn't after rereading OP) then yea, snippity, even though it went 20-40-1k. Still, it's ok to give pause if it's a truly deep spot with the 3rd nuts as suggested above given a bet of this size otherwise tends to narrow things. Club game with big buy ins late in the night, yeah, that's a different story.

snap call and ask to run it twice lol

Game generally plays like 2/5, especially as the night goes on. a lot of stacks 500+, some 1000+, straddling and large open sizing. This hand played more like 1/2 though, in that there was no straddle and the open raise was $12.

Let me know if this has run its course and I'll give results.

I actually fold here. This is one of those "slightly ahead or way behind" scenarios and there's very little dead money in the pot, given his ridiculously huge 3bet shove OTF.

As others have pointed out, we're actually a slight underdog against a hand like 86hh. I also highly doubt villain is shoving an overpair here (unless it's 66) and I don't think 2pair shoves either.

I put him on sets, A2, 76, 66 and monster draws (NFD + gutshot, FD + open ender, etc.). So I fold this deep.

I mean, statistically, this was (literally) the 5th best flop you could have asked for with dat hand (222, AAA, AA2, 22A are the only ones ahead). An over bet here is huge and since you describe the villain as wide and positionally unaware, 6-7 could easily be in his range. But so could overpairs (you say he over values his hand, and I would raise here with Qs up (wouldn't shove that hard, but I would think I have the best hand most of the time if I were the villain). I have a lot of sets. A drawing hand is possible, but it feels really weird to all in on a draw, even with 2 streets of action to see. If his goal is to bloat his pot because he wants to make sure his "hit flush" gets the most from you, he should just call and let you b/r into him.

It's one of these scenarios of why hands like this belong in the muck when you aren't checking the option. I wouldn't mind seeing results though, but knowing how these threads work, you either call and he scoops you or you fold and he shows a bluff (super cynic, I know)

Against this range this is a clear call. $165 in dead money ain't nothing.

I'm balancing my posting range Results are that H thinks for a bit and calls. V shows 33 for bottom set. Run it twice and H wins both. V said something to the effect of thinking that H had a draw and that V wanted to get H off of it, and that he didn't think H would raise with a hand that strong. Also remarked that he knew he'd punt off a huge stack to H at some point and even had said so.

Obviously V's shove is awful. I think he thinks it's for value, when actually it's an accidental bluff, because he could get me off of a set of 4s here. Never, ever getting called by worse. What I think happened here is that V is implicitly uncomfortable playing this deep, especially OOP against H, and is trying to end the hand on the flop to avoid difficult decisions later. Of course, that means he makes a bet that never gets called by worse, and gets called by most of the better combos, as I'm never folding top set or top straight here, and as demonstrated am probably calling bottom straight too.

The way he played, I am calling that with any straight, and if I get coolered because he went crazy pre with a 6-7, I get coolered.

Glad it worked out, I definitely understand being deep though, and am not super comfortable myself in positions like that. It's easy to talk about why your call was the best EV, but another thing to put $900+ in front of you to gamble with a wide V could have you drawing dead, or be behind you, but with out.

I think my calling range here is top set and any straight. With top set at worst I'm a 2:1 dog, and I'm often way, way ahead. Middle set would be a very tough, and probably is a fold though it would be hard to let go of it in real life.

I will say one advantage I have over V here, over a lot of Vs in my game, and probably over a lot of folks in this forum is that I'm very good at divorcing myself from the amount of money at issue in a given pot. I'm playing purely recreationally with money I can afford to lose. The weird thing is that V's discomfort with the amount of money he had in front of him and fear of losing it on later streets if he got drawn out on caused him to get it in on the flop as a 2:1 dog against a range that's crushing him.