I would recommend another approach:
JFK-FRA on SQ (A380), FRA-BER on LH. Return, BER-EWR on UA, then EWR-ORD.
This appears to be around $6700 on a random set of dates I checked in July. This way you get the far better A380 product outbound (adds a stop though) and a flat bed on UA on the way back. The LH product is not a flat bed - it's angled lie flat seat.