What a wonderful summary!!! Well done!!!
Indeed you are very right, too many people ask the same questions all the time.
I try to think of if there is anything than could be added, but pretty much everything has already been wonderfully covered.
Maybe two things:
*They are actually doing some construction work on the Thameslink during the autumn (don't know for how long though). Anyway there won't be any direct trains all the way from Luton (northern London) to Gatwick (southern London), they will all terminate at Kings X if I got it right.
*When taking a Thameslink train from Gatwick there are excellent interchange possibilities at London bridge. For example it is possible to change to a train going to Charing Cross (a stone's throw from Trafalgar square and five minutes walk from Piccadilly circus) without even having to change platform at London Bridge.
I look forward to when the DLR extension to LCY is completed, it will make the transporation there so much more convenient.