It seems like we have a very similar (spooky) travel pattern! As I'm looking to do the same and I believe we cross on our CE trip! This keeps me Silver each year but wouldn't achieve this without the incredible knowledge from the people here, anyway...
How about an Ex-OSL to JFK with part pay Avios so could bring the price down to below £400 ret in WTP then UUA or AUP to CW. Still netting you 200TP's. CW is only needed on the return leg if you're happy in WTP plus on a day flight to JFK.
If you drop the last leg accidentally this would get you the 3 BA qualifier of 4 you need.