2/5 live game, fairly deep.

3 limps,
96cc in cutoff with $4k stack
Open to 35
Bb and 3 limpers call.

Flop KcTx2c
Checks to me, bet $125
BB calls rest fold
Turn 8x
Check/ bet $225/ BB min raises to $550 w/ 1.1k behind

Lots of history with BB, he is somewhat thinking player, typically very passive against me with strong holdings, as I have pretty aggro image.

My first question:
What would we do with our top value range here? Do we go for the flat with hands that block some combo draw hands that he decides to min check raise and jam those that do not? Do we jam all strong value, or do we flat our strong value?

Second question, based on answer to above question, what do we do with 96cc here?

My initial thoughts: I would probably jam most of my value hands KTs, KK, TT, AK and AA that don’t include Ac to deny equity against any combo draw that decides to put in the check raise?
And in doing this, should also probably jam AQcc, AJcc, QJcc, Q9cc, J9cc, and 96cc.
Is this poor logic?

What would his range look like for flat bb x/c flop x/c/min raiser turn? I have played hundreds of hours with this player, and do not think ever once has he taken betting lead away from me when he has had a premium holding, as I may have a reputation for blasting off.
I guess the main question here is what would we do with each of our value hands, and then in turn, what should we do with some of our bluffs.

I hope this made some sense, as I am typing this on my phone, and appreciate any feedback

Thanks.