Coff,
The best answer I can give to your question (how fast can the F-35 get from jet borne to wing-borne flight) is 'actually quite quickly'. (Sorry, but I don't know the precise answer).
It's important to note that the aircraft will rarely go from a hover to forward flight in an operational sortie, except if it has to abort a hover landing. All operational sorties will use a STO, not a VTO.
In a STO, the actual transition is controlled by a single selection made by the pilot after leaving the ground, using a switch on the left hand control 'inceptor'. The vehicle control systems systems then take over and do all the clever scheduling/door closing/flight control stuff. That takes a fixed time, I think it's under 15 seconds. All that time, the aircraft is climbing away at a fair rate.
Vulnerability is an interesting issue - a STOVL aircraft's timelines from arriving in the overhead to landing, and from starting takeoff roll to up and away are really quite short, in most cases a bit shorter than a normally loaded conventional jet. Yes, it's going more slowly during the transitions, but it usually occupies less airspace to do it.
Best regards as ever
Engines