The C-130 has proven itself eminently capable of landing on a carrier.
When the S-2 Viking was retired, the Navy didn't really have a good replacement for anti-submarine ops - but anti-sub warfare had also fallen in importance.
Suppose there is a resurgence in need. The Navy has an excellent ASW aircraft in its inventory; the P-3 Orion (modded L-188 Elektra). It's not made for carrier operations, but then, neither was the C-130.
Suppose we sort out the smaller details, like making sure the P-3 can refuel from carrier-based aircraft like the F-18 (and thus can take off and immediately tank). This must be a rolling-on-tires operation; cat launch or tailhook recovery is out of the question.
If the captain can guarantee 35 knot headwind, could the Orion do a "rolling on pavement" takeoff and landing off the carrier? If needed, it can use the whole deck, obviously it would work better operationally if it could use the diagonal strip.