Courtney,
Excellent point well made - there is a whole world of difference between the F-4's hook system (stressed and designed for repeated engagements in a wide variety of attitudes, and able to be repeatedly raised and lowered) and the F3's emergency 'one time only' design. You also make the excellent point that you need a fair bit of structure in the aft fuselage to react all those hook loads back into the airframe.
LO, the aft frame location on the F-35 wasn't driven by the F-35B variant. It was driven by the need to develop a single common airframe layout for all three variants, at the lowest possible weight. The main aft frame also carries landing gear loads as well as engine thrust loads, plus taking the rear wing spar. That's a common arrangement these days.
No, there wasn't a standard-minimum wheel to hook distance. And tail hooks are attached to end of a load bearing structure that is specifically designed to take tail hook loads. That structure only exists to take the hook loads, and it's usually massive. F-35C is no exception, with many hundreds of pounds of extra metal down aft for that very reason. The keel between the engines on twin engined designs like F-18 was only there to take the hook loads - that's why Courtney's point about the F3 is well made - the F3 really didn't have much of a 'keel' because it didn't need one.
By the way, as massive as the structure is to handle the hook loads, it's as nothing compared to the tons of metal needed to handle catapult loads - but's that's another story....
I was involved with the T-45, and I can tell you that the additional longerons needed to handle the hook loads were very, very substantial. BAE couldn't use a single keel beam because of the engine removal panel.
The point I'm trying to get across is that this deck landing business is hard, and the systems and solutions needed to do it reliably and safely are hard to design. No, really hard. LM very clearly did not get this hook system right first time - but my bet is that they'll fix it.
Hope this helps
Engines