I very much suspect that they will go for a 4 engined aircraft and it will be cheap, hence a C-130 derivative being most likely.

4 engines are no longer necessary or even desirable. Might have been back in the 1950s-60s when experience with turboprops was limited, but history has shown that turboprops are extremely reliable. AFAIK, only one of the ~120 Atlantic/Atlantiques was lost due to engine failure.

A C-130 will cost a lot more for this role than any of the two-engined options (Atlantique, C-295, ATR-72). The only way this would make sense would be to rerole RAF C130Js, since they may have lots of “free” airframe hours remaining (the limiting fatigue constraint likely being landing cycles/low altitude tactical ops, neither of which is a big deal for an ASW aircraft).