The Sukhoi option?
It's late a night and I am feeling creative - this idea must have been done to death a million times but...
Having seen how the Sukhoi Su-33 launches from the Russian carriers without a catapult, just brute force and a ski ramp - I wonder whether the LHAs & LHDs could be adapted (together with arrester gear) so that the USMC could take the Dave-C?
In design, they have a family resemblance to the RNs 'Through Deck Cruisers' (remember the dodge to not call them aircraft carriers) - no angled flight deck though so I guess they would be launching OR recovering but not both.
Having looked at some of the thrust to weight ratios put forward about the F-35, they are not a million miles away from the Sukhoi.