HVAL,
Thanks for coming back - hope the pesto turned out right!
The basic problem with the Harrier concept (one engine providing both lift and thrust) was that to get the thrust required to allow a sensibly capable combat aircraft (around 35 to 40 thousand pounds) to hover required an engine just too big for sustained supersonic flight. Cross section got too big, and using hot gas to provide the main lift effort just didn't work.
The other problem with a big engine in the middle of the aircraft, driven by CG, is that it displaces lots of other stuff you want to put there. One of the major issues with the F-35 weight saving effort was to redesign the aircraft to put lots of bits and pieces back in their proper places. Having a dirty great engine in the middle makes that even harder.
Oner good thing to take away from this thread - STOVL is insanely hard. Supersonic, stealthy STOVL is even harder. Getting the F-35B to where it is, and making it part of a whole family of combat aircraft, is even harder than that. And here's the thing - this achievement (and it is a massive achievement) has included many extremely talented Brits doing things that our American friends could not do. Once in a while, it would be nice to celebrate that.
Hope this helps,
Best Regards
Engines