It isn't really that the JC1 design can't operate as a platform for F-35B's, its just very limited as one. If all you need is 1-6 aircraft, it can probably do that. Temporary carrier, CAS, deterrent, training etc. But it wouldn't be a CVL. It would be a LHD. At this stage its unproven, but that will change with time.
The Japanese from what I can see are planning to operate up to 10 F-35's from a modified Izumo. (probably conservative)
The Italians seem to be up to 16 F-35's from Cavour.
The Italians also seem to have a larger LHD in
Italian aircraft carrier Trieste - Wikipedia. Which should displace 33,000t, 2 Mt30, full LHD capabilities, 245m length. 9 helo spots, no jump, 25kt speed. Two island layout, edge lifts, I would imagine it would be quite capable.
I would say take a good look at Trieste and benchmark it. We might be able to consider something similar as a 35,000t LHD based off the existing JC1 design, lengthened, bigger lifts, Mt30 propulsion. The Spanish also had plans for a CVL before the money ran out.
Up from there you talking America class, QE class etc. Which then puts you into the realm of regular operation ~20+ f-35bs. Both are probably capable of well more than that particularly QE. But that exists in the $5 billion+ usd for the purchase ship alone, 700 crew for the ship alone. That gets us 1 ship. We would then need to set up training and logistics for that one single ship. For what would this carrier be for? Projecting power way out in the deep blue sea? Overpowering other nations air defences and regime change?
I just don't see the argument for a large CVL stacking up.
Some sort of LHD I think it entirely plausible. We could make some modifications to the JC1 design to enhance aviation. Or choose a LHD/LHA that has already been modified (Izumo/Trieste).