I would try the following:
1.) Call again and try a different agent.
2.) Point out that from a fare calculation perspective the 12 hours in NYC is a connection. Assuming you are travelling on a LHR-LAX fare, youre fare calculation should be LON X/WAS X/NYC LAX. Also point out that UA's definition of an open jaw is
OPEN-JAW TRIP--MEANS ANY TRIP WHICH IS ESSENTIALLY OF A ROUND TRIP OR
CIRCLE TRIP NATURE, BUT THE OUTWARD POINT OF DEPARTURE AND THE INWARD
POINT OF ARRIVAL, OR THE OUTWARD POINT OF ARRIVAL AND INWARD POINT OF
DEPARTURE, ARE NOT THE SAME.
Since NYC is not neither an INWARD or OUTWARD point of DEPARTURE or ARRIVAL, LHR and LAX are, it can't be considered an open jaw .
EWR is not the same as LGA/JFK. EWR fares are totally different than those to LGA/JFK.