OAP,
I apologise for not being clearer - by 'oversized' I meant that the engine had to have a very large diameter - this led to a fairly fat fuselage and a basically subsonic design. That was a challenge looking at the UK's firm requirement for a next generation supersonic STOVL aircraft.
For a combat jet, LM's view was that the right place for a single engine is down aft. This minimises jet pipe losses, allows more options for intake placement, and frees up the central structure for stuff like weapons bays (if you are going for stealth) as well as fuel. I am inclined to agree, but I know others might differ.
The British preference for aft mounted engines on airliners was driven in part by a desire for very clean wings to attain high cruise speeds and long range, with quieter passenger cabins as a useful by product. This layout was structurally inefficient, and led to substantial extra weight (which reduced the range). The situation is very different with combat aircraft like the F-35. The engine thrust mounts are closed to the main wing spar and also the undercarriage attachments - making for what should be an efficient structure.
The Harrier design solution included multiple small fuel tanks built into the fuselage to replace larger but fewer fuel tanks - they worked, but could never be very weight efficient. They also leaked. The UK's many efforts to design a supersonic ASTOVL design with a centrally mounted engine never delivered a feasible design - and I got that opinion from a senior BAES designer.
You are spot on that the right compromise is the key. My answer to your question 'have they got the compromise of the F-35 badly wrong' is 'no, I don't think so'. Again, I know others will disagree.
My view is that the design has concentrated on high end sensors and information capability, and systems integration with the weapons. I think that's a key attribute. They have gone for an 'LO' design, not a 'VLO' design, and have not pursued the highest end of the manoeuvre spectrum. Again, I'd back that call.
Most importantly for the US, they have produced a common family from one aircraft that replaces many legacy platforms. The savings are planned to come downstream as the production lines roll and the support systems are delivered to reduce through life costs. That's the plan. Again, I know others think it's a rotten plan.
Hope this helps a bit,
Engines