I would think basing them aboard ship will be dependent on if they are able to be moved to the hanger.
As the Hyuga-class only have central deck elevators. It would depend on their dimensions. Folded, the V-22 is 63 ft long & 18 and 1/2 ft wide.
Now, I don't know for certain if the H-60 or AW101 the JMSDF use have folding tail booms. But the H-60's fuselage length is under 51 ft. Whereas the AW101 is just over 63 ft, but when folded for stowing in is under 52 ft long.
The elevator dimensions aren't as much of a problem on the Izumo-class, as along with one central decl elevator they have a single starboard side one.