BBB,
Lufty is your friend. Use the direct EDI-FRA/DUS flights, then pick up TATLs there to/from ORD or BOS. That gets you across the pond with one connection, and also means that you only have two flights before/after the stopover.
Plugging a few trial dates in miles-and-more, there's plenty of TATL availability, certainly in J, for 4 pax - fr'instance out 30 June LH432 FRA-ORD then back 18 July on LH437 ORD-DUS, or LH423 BOS-FRA. Reasonable connections for EDI-FRA-EDI (well, a four hour wait on the inbound). Then you just need to throw yourself on the mercy of the ICC for the internals, on CO/UA/US, which should be okay.
Actually, just remembered the problem with Lufty married segments. All these flights are showing up okay on M&M separately, but the ICC may not be able to tie them together. But should be worth a punt - just talk them through each stage, starting with the TATL and then adding on connx at each end. Let me know if you want me to look at specific dates/routes on M&M... I've seen bmi award availability match M&M.
Good luck !