Now lets see an actual SV-22
While Osprey ASW is theoretically do-able, it probably wouldn't be using a dipping sonar. Ospreys are not particularly efficient or good in the hover, and using dipping sonar means lots of time spent hovering. If someone was stubborn enough about it,
SV-22s using dipping sonar would absolutely be possible. Enlarge the access hole in the belly for sling loads so that the dipping sonar can pass through that spot.
It'd be some heavy modifications, but I'd install the AFSOC "combat doors" with drop tubes in them on both sides aft of the wing. Yes, I know that Ospreys don't have doors there. That's part of what would be so expensive:
making the space to install the combat doors.
I'd further replace the rear ramp with one that had Sonobuoy tubes on both sides and leaving only a walkway up the center of the ramp. Split Common Launch Tubes on the rear ramp would be another option. MC-130s have 10x CLTs in a single block, I'd run 2 sets of 4x if possible.
Torpedoes and/or depth charges would need to be carried either on the wings or on the sponsons.
EV-22 (I vote Erieye, although that pesky wing "fold" would make it difficult).
I mean, there's a hinge pin in the wing fold, I'm assuming that it's hollow and you could rig the radar leads through that point. Have a non-rotating pin that comes up to the radar beam to support it, and wrap an aerodynamic shroud around it that is attached to the pin.
Probably have to anchor the beam to the top of the tail fins at the rear, though.