PriFly:
Good points. Part of your idea requires a tailor-made detachment of SH/MH-60 variants to plus up the Marines.
The normal Air Group on an LHD/LHA is cargo-people haulers and attack helicopters, and maybe even some Ospreys. Plenty of eyeballs to help in a search.
Ship has good C2 capability, air traffic control facility for others coming from farther off, and good sized boats that the ship can launch to recover bits and pieces as needed.
Based on what I am looking at on the map, you'd still ned a tighter search area first before the LHD's strengths could be best utilized.
Without wanting to sound the conspiracy theorist again, is it possible that these pings are incorrect and the aircraft is actually on the ground somewhere?
Possible? Given that most of us in the general public only have bits and pieces of information, and based on those bits and pieces ... yes, it is possible, but I won't take it to Vegas and lay down the rent money. Feel free to consider how that "northern arch" referenced to the satellite ping (go back a few pages, some posts have that picture in them) would be possible AND how it would be possible without being noticed somewhere, somehow.