"The F-35C is still a ridiculously expensive way to deliver the same STOL"
The F-35C is simply the "navalised" version - it's not expressly designed for being STOL, although it has larger wings to increase payload and range, and allow for better low-speed control for carrier landings. The landing hook will take care of short landings, and catapults of short takeoffs.
Most planes that were not exclusively designed for the Navy had a specific "navalised" version to ensure they can cope with carrier operations. That usually means features that are useless (more complex, heavier, and/or more expensive) on land-only version, like sturdier landing gears and tail hooks, foldable wings, etc.
Also the US Navy uses a different air refueling system than USAF - the same used by most other air forces (probe and drogue ), and the C version is also designed for it.
You can't simply get an A version and have it operate without issues from a carrier.