Dat,
The straight answer is (I think) no, the F-35B won't be anywhere hear as bad as the F-4K. Let me explain.
The F-4K had two Speys, each rated around 12,000 pounds thrust dry and 20,000 pound in reheat. As far as I can see, most F-4K cat launches were in reheat, so there was about 40,000 pounds of very fast and very hot gas involved, withy the nozzles just inches from the deck.
The Ark Royals' JBDs were (I think) actually designed for the ill fated CVA-01 and the P1154, and were designed to handle a very hot jet efflux striking the deck. They included water cooling for both deck and the moving plates, which included a short side plate each side of the main JBD plates, designed to contain the hot gas sheet flowing out across the deck.
The F-35B launches with the main engine operating in dry thrust at around 18,000 pounds thrust, because 50% of its power is being extracted via the drive shaft to power the front lift fan. The engine is deflected down around 10 degrees at launch, with the nozzle some feet above the deck.
So, by the time the F-35B main engine exhaust hits the deck, it is already spreading out, slowing down and cooling.
The reason I can be fairly definitive on this is that I worked closely with the very good BAe team at Fort Worth and Warton whose task was to predict, model, validate and finally confirm the F-35's external environment (for all three variants) in all required operating areas, including carrier decks and short strips. They were helped by a similarly very good team assisting the CVF guys in the UK with some excellent CFD modelling.
I hope this helps, and also helps illustrate to some readers that the team producing the F-35 have taken a thorough and professional approach to delivering a powerful and substantial powered lift aircraft into service. Put another way - they aren't numpties.
Best regards as ever to all those Brits doing the F-35B business,
Engines