What is of course very tempting would be to do GVA-LCY-JFK just to avoid LHR.
1) Shame that GVA-LCY is operated only by the competition (LX and AF).
2) How do you do flight connections in LCY? As far as I can see you actually can't, meaning you have have to go through immigration, collect bags if you have any, pass Go, do not collect 200£, check-in, immigration, security, etc. Still all this is usually pretty harmless in LCY.
Tempting though