Have you ruled out 3 betting here?
Seems to me that you are almost always ahead on the flop here.
would 3 betting big here be an option worth considering? or do the stack sizes make this option a no no?
I'm just thinking that if you overbet here, villian would have to fold all possible hands that beat you, such as 8x, 55-77, so, in theory the only hands he then jams with are the flush draw, which you are in good shape against.
So, you three bet as a semi-bluff. Ie-you get the hands that are beating you to fold, but you get it in against the hands that you flip with such as

.
Is there any sense in this line of thought, or is my head still in the clouds, having just woken up?
There is a big problem with this, and that is that our equity vs the weakest hands in his range is ok, and vs the strongest part we're totally crushed. Lets say for example we get him to spanner it in with Q9o
ProPokerTools Odds Oracle Results (2.05 Professional)Holdem, Generic syntax
Board -

PLAYER_1 44
PLAYER_2 Q9
95040 trials (exhaustive)
All-in Equity
We have 70%,. Unless he decides to go of his lid with A4, 3* or 33 specifically (and he doesn't peel too many 3*s from the BB even in 6max) then the best case scenario is we get it in 70/30. I agree with DM when he says people are not going to be too likely to spanner off on a board texture like this, in a spot where you have a decently wide/feasible 3b/call range on the flop (most OP's are easy to get in with the 2 being the paired card, flush draws etc) and he's going to be under it vs anything legit you wanna 3b/call on the flop.
So, you three bet as a semi-bluff. Ie-you get the hands that are beating you to fold, but you get it in against the hands that you flip with such as

.
Is there any sense in this line of thought, or is my head still in the clouds, having just woken up?
The problem with this is that when we get in vs a legit value range (8* if he's gone mental, slowplayed QQ+) then our equity is so poor
ProPokerTools Odds Oracle Results (2.05 Professional)Holdem, Generic syntax
Board -

PLAYER_1 44
PLAYER_2 8*, QQ+
908820 trials (exhaustive)
All-in Equity
These spots where it's close the main "room for error" if you like that you have is how much equity you have vs the average legitimate value hand he has and in spots where you're crushed (like here 10%~) then the maths is usually pretty brutal on the long term profit of the play. Because he needs to show up with Q9o/KJhh considerably more than he shows you something that smashes us.
Ithink this is a spot where your flop 3bs can be pretty polarised, speshly as the value range you're repping is completely reasonable, i wouldn't use 44 to bluff with, perhaps use it to call down sometime - depends what else you've got you can call him with, so I think for the most part I just fold here and use hands like overcard hands to start bluffing with
ProPokerTools Odds Oracle Results (2.05 Professional)Holdem, Generic syntax
Board -

PLAYER_1 KhQ
PLAYER_2 8*, QQ+
582120 trials (exhaustive)
All-in Equity
granted your under it vs AJhh