I actually think that both the 77 hand is pretty standard.
I think 77 is fine shove for resteal. He's utg 4 handed, that's the cutoff and utg. If he's utg 6 or 7 handed and tight then I could go for a fold.

King-4 hand is kinda meh. If you have a read that he ever spews you can call. but for 2.5x pot there are alot of 2-pair/set/slowplayed stuff in his range.
I do agree that you just have to release vs a flop bet with like bottom pair no kicker or second pair no kicker facing a bet on the flop multiway.

anyways best of luck with your operation.