Coke, a very good question, Mate.
F-15 only realy became a serious option when we were already committed to (what was then called) Eurofighter. The F-111 tradgedy was a different story and I don't think we ever really had a gap for F-16 to fill.
But that doesn't answer your question. If you ignore all the banter and stuff (I'll call it "stuff" for now) we asked for a long range interceptor and got the F2/3. Apart from the ridiculous failure to make the aircraft totally automated and simple to operate, BAe did what they were supposed to do. And, our crews acquitted themselves superbly in wars and excercises - sometimes much to the surprise of our allies (you decide which ones).
I have to admit to being involved in various evaluations in some of the choices you refer to and, to me, the issues often came down to what we would have bought - apart from just ("just") buying the aircraft, what would have bought and what would we have to buy (and keep buying) to have a supportable operational platform?
Probably, buying US or French or Russian wouldn't have been as bad as many claim. The effect on the rump of British defence industry would have been disasterous.
I'm looking forward to this thread.