Glojo,
Perhaps I can help here - I worked on the JSF programme with the specialist ship suitability team, and have a pretty good knowledge of the arresting hook system.
The X-35 programme was, as said here before, a demonstrator for basic technologies, and that didn't include the complex matter of testing the arresting hook system.
I worked with the team designing the hook and can confirm that the design they came up with (after a number of changes) was fully approved by the many US Navy subject matter experts from NAVAIR who conducted a string of reviews. (The US specification does not, as far as I know, specify a minimum distance between gear and hook - it does specify around 30 other parameters, all of which the design met).
The whole business of getting arresting hooks to work is actually highly complex and difficult. The USN make it look easy because they are extremely good at it.
LM are trying a redesigned hook point and a new damper to regulate hook bounce. If those don't work, they are going to have to design some form of extending hook or move it aft - and that could be a real problem. However, they are not there yet.
Finally, the arresting hook issue is not the biggest faced by the F-35 programme - read the Congressional quick-look report for the rest.
Hope this helps, best regards,
Engines