EM - To begin with, what you do with the LHA/LHDs is (drum roll) what they were designed for (the basic hull design of even the newest ships pre-dates the Harrier in USMC service) which is to transport Marines, weapons, and vehicles in a warship-hard hull and get them to shore and support them with LCACs and helicopters.
They do this very well, the LHA-6/7 mongrels without a well deck having already been deemed a mistake before the first one is complete.
They are not very good aircraft carriers because they have inadequate hangar space, JP and weapons capacity, and narrow decks. The not-much-larger UK carriers can support a much bigger air wing - 35 F-35s plus AEW assets, versus 22 on the LHs if you push all the helos overboard.
Also, when the Ministry of Truth at Fort Worth says that the F-35B can carry 15,000 pounds of ordnance, I think that they mean that its various station capacities add up to 15,000 pounds. Real world? Maybe I could load the internal stations (3K), carry the gun pod (makes it 4K) and two 2K bombs on inner pylons (8K) and two AIM-9s (call it 9K). My operational radius will be well under 300 nm, I will be well subsonic and non-stealthy.
Supercruise? No, the F-35 was not designed to sustain >M1.0 without afterburner and contrary to various shills, cannot do so.
Kicks the Harrier into the long grass? Well it should, given that the basic design of the Harrier is now 55 years old and that it has never had a from-the-wheels-up development program - it's still an evolutionary development of the first P.1127/Pegasus.
WhiteOvies - Wheeler raises a perfectly valid point. As you note, the VL pad at Pax is AM-2 mat, but laid over concrete as a heat-shield rather than as a structural surface over dirt or cr@ppy asphalt. The VL pads at Yuma and Beaufort are made of heat-resistant concrete. There's some notion of a "creeping vertical" landing but there is no word as to when that will be demonstrated at all, let alone on the equivalent of a 3,000-foot-somewhere-ending-in-stan runway.
The Thermion coating reflects one of the two LH-related heating questions, which was the effect of F-35 exhaust on non-skid surfaces. The other was the long-term effect (if any) of heat and blast in terms of thermal/mechanical fatigue.