I know we have a ton of equity with our hand so we can either c/shove turn or b/c profitably. However, what's the line that maximizes FE in your opinion?

If we c/shove, our range will look like it contains a lot of FDs (both hearts/spades) and we may get hero called as a result with a higher frequency. If we check turn and villain checks back and river bricks, are you giving up or stabbing? What bet size?

If we bet with the intention of bet/calling, we're in an uncomfortable spot if villain just calls and river bricks. Are we jamming if this happens? Given how many draws will miss, I feel like we will get hero called by anything that villain called turn with that wasn't a draw.

Also,
Let's pretend we have AJ+ (villain almost always 4-bets QQ+ so AJ=QQ), what are your thoughts on c/jamming turn to rep a draw and trying to get called light? Or do you prefer betting turn? If yes, and river bricks, are you jamming trying to get hero called or are you checking and trying to snap off a busted draw from villain?

In summary,
1) what's the line that maximizes FE in your opinion?
2) If we check turn and villain checks back and river bricks, are you giving up or stabbing? What bet size?
3) If we bet turn and villain calls and river bricks, are you giving up or jamming?
4) If we had AJ in this spot, what's your preferred line?