I've flown in coach on all three of them (AY and SR to Moscow, as well, albeit my SR experiences date back to the "old" Swissair rather than the new Swiss).

My personal favorite is Finnair, due to very convenient connection in Helsinki (except on Sundays, when there is only one afternoon flight from Helsinki to Moscow) and consistent quality of in-flight service. The downside here is that your JFK-HEL flight is on AY metal, MD-11 without MRTC or power ports in coach. Usually, I'm able to secure an exit row seat, which has huge amount of legroom, especially in aisle. Last time coming back I've been semi-upgraded to business (business class seat with coach service). Food on that flight was terrible though (awful barbecue chicken).

Your AA/BA option should be OK going to Moscow, but on the way back you'll have to overnight in London, as the earliest BA flight from Moscow to Heathrow leaves Moscow in late afternoon.

Your AA/SR(LX) option will require more than 7 hours connection time in ZRH on the way to Moscow, and you will arrive in Moscow after midnight (at the Domodedovo airport, not Sheremetyevo, as AY or BA). You should be OK on the way back, with only about an hour connection in ZRH.