I agree, YQ/YR is an incredible pain in the ....

So since you'd be saving some $800 per ticket, you may consider flying into a different european city on an airline that doesn't chart YQ, and then buying a cheap round-trip on a european low-cost carrier.

(1) Fly UA from JFK to literally anywhere in Europe
(2) Buy a round-trip rail or LCC ticket.

That way you can even consider your arrival city a free stopover. Spend a day or two there if you're flexible. What dates are you looking at, out of curiosity?

FWIW, UA charges $0 YQ/YR, LOT (LOT) charges only ~$320YQ, and Turkish (TK) charges ~350YR. This is much lower than Lufthansa, Swiss and Austrian's $806YQ.

See if you can make something out of that. Try a multi-city itinerary, or a round trip to a different european city in combination with a low-cost carrier. It is, after all, only the transatlantic leg that will set you back any big money most of the time.