Well, I can see that 1,200-1,500 foot runway including resupply by MV-22 Osprey and CH-53K, not C-130J.
As for the matter of AEW - the USMC has been looking into that, with several options (such as TOSS) - again using the MV-22.
And they are also preparing to extend the operational range of the F-35B - Osprey again, curiously enough.
This would allow additional F-35bs beyond what arrived in-theatre with the LHA/D to stage in from elsewhere to the flat deck, and to the newly-established FOB.