As you pointed out your range hits that board super well.
Therefore I think you can only make villain mistakes by building some history with him on that kind of board.
If you bet your whole continuing range in a size that allows you to jam any turn potsize you put his whole stack at risk without allowing him a showdown all the time (if he never check ships that flop). What I mean is that if you just pot it, every time he finds a call he is also getting to realize his whole equity.
By betting he can call, trying to realize his equity, but you can still profitably jam almost any turn, leaving him at a guessing game again.
If you have implemented that strategy and shown some good hands you can start to try and get folds both OTF and OTT with hands that he would actually have enough equity to call.
The question is if it's worth it in a rather large playerpool where potentially the spot doesn't come up often enough

Honestly ingame I snappot this probably every time.
But that will result in him folding a lot and he's not making a mistake since we crush that board so hard.
If you bet small and he finds a fold you forced him to make a mistake because he's not realizing his equity when given a good price. You can still check back some turns. I doubt he'll just put you all in OTF, as you said betting small looks like a trap and even when a turn seven hits, he can't just donk all in as he's so capped and your not, therefore your not making any incorrect folds or calls.
I also think your not arguing logically; you wanna pot as you think it's looking more like a bluff when really you have pretty much no bluffs in your range and then you make an argument for villain thinking we might bet out strong range small.
As for ppl checking their AA with some backup. I don't think it happens too often.

I think often people are too focused on trying to get an opponent to make a mistake in a specific hand. In this situation it will be almost impossible to get the opponent to make such a big mistake as stackingnoff.
What you should be looking at is leading him to make a mistake while playing against your range. This would involve him overfolding his aces with good equity vs hands that you have that don't actually crush this board. So think whether you can have a bet sizing that A) allows you to bluff profitabley in the same situation with a different hand, or B) have him call when you still have more equity on a different board.

Remember if he has a sniff of equity outside aces you will likely end up getting it in either way. So you should be planning your bet sizing with regards to the rest of your range. You should be able to overbluff this spot.

First off I get your idea of splitting your range now and the different bet sizes you wanna employ.
But I'd do that in spots where you actually have more different groups of hands. As you already said its pretty hard to find pairs that don't have anything to go with them. When we hit a board so hard and our opponent doesn't, in my mind it makes more sense to have one betsizing for our whole range to not give away any further info.
Ofc you can split your range and try to balance it by moving a hand as strong as yours into the potting part. But does that shot come often enough so that you could profit from having different ranges with different betsizings?
When you bet with one small sizing you could at least get him to fold because he has poor visibility with most of his range or to get it in often drawing very slim. It also makes you very tough to play against because even in 4bet pots he might have to pay multiple streets against you oop.

Maybe we have diff definitions of a bluff in this spot.

If i had KKT5 no fd here for some reason, id pot it. In a way im bluffing but its more of a semibluff and were not folding if raised.

If i had something like TT44 no fd id probably bet half pot and fold if raised.

we have 67% vs AAand he needs 37,5% eq to stack off if spr =1.5.

Its hard to say which sizing looks strongest when u bet. Id say a small bet will look like u have some monsters, some bet folds, a pot bet looks like ur never folding, but will mostly be draws and 2p and prob never a str8/set or big combo draw. 66-75% could be a combination of the above.

Depending on our sizing, wed prefer

A) He jams in AA no draw with 27% eq

B) he folds to a tiny bet

C) worst case he xc getting a good price and pot donks non clubs/Q/J/K/T/8

So with that in mind, i dont like potting it, betting hp or smaller might be risky vs a sticky opponent, as he might be tempted to peel and the natural instinct would be to fade the flushing and str8ning cards and donking or calling on a brick (if u shove an off suit 5 fex).

So id prefer 60-75%ish pot bet if u have no hist.

Vs a sticky, or even better a semi spewy opp that thinks ur capable of stabbing with air id bet 33-50% pot and hope he stacks off.

As far as ur range goes tho. Unless ur calling 4bets with AKLLds/ABBL the only compl misses u have will be double pairs no fd or set. And even a weak hand like JT65 no fd would prefer potting it, maximising feq vs AA but forced to gii so potting anything or most of range that u bet makes sense

i agree we are bluffing with KKT5 no fd vs AA if we're betting, but were not gonna fold if he jams so were kinda semi bluffing pushing our draw. JT65 no fd is a better example, bc we could actually b-f KKT5 small vs some ppl

if youre gonna get that specific about your range id recommend plugging in your range in PJ and see how many hands that have less than 37,5% eq vs AA. my guess is that more than 50-60% of your range will want to v-bet vs AA, semi bluff vs AA, protect vs AA. so id rather make the minority of my range adjust to the majority so to speak.

checking back this hand vs villain seems intuitively wrong, so id rather half pot this hand then and half pot my entire range.

the url isnt working in pokerjuice?

well id recommend manually typing in your 3b-call4b range and see how many hands wanna pot-call it off (which id do with probably anything that has 25-33% eq or more vs AA)