I would think that LH2 would be the way to go because of power density. Certainly a lot of technical hurdles to overcome, but as you say, the Navy is capable of fielding the expertise (and paying for the solutions).
Note that IMO the LH2 would only be applicable for smaller ships. Anything big is already going to have a nuke. I suppose it would also be likely to use onboard reformers and derive the H2 from oil. That would at least let them use existing infrastructure.