If it says an impossible connection for the LGW-PHL flight, then it's very likely that you don't have enough time for the minimum connection time between the SIN-LHR flight and the LGW-PHL flight.

It is perfectly OK to backtrack not only within a continent, but within any of the 3 areas.

You've got a couple thousand extra miles on a 29k RTW routing and plenty of segments to work with. If you have extra time in Europe, you could certainly do some mileage running. Also, unless you're wedded to flying US, you've got lots of alternative trans-Atlantic routings (esp if you're flying in C).