If the requirement for the JSF had not included STOVL, then the aircraft would have looked completely different ...
Why completely different? Can you state any reasons?
... and may well have been twin-engined.
No. The primary requirement for the F-35 is to replace the F-16. Count the power plants on an F-16.
The primary reason for one engine instead of two in a smaller fighter aircraft, assuming a large single engine can produce the same thrust as two smaller ones, is that the large single will yield better specific fuel consumption, lighter weight, and lower cost.
Consider the trend in civilian airliners: very large twins replacing aircraft with three or four motors. The same considerations are at work in both cases.