I've now talked with BA ad nauseum about this and they really aren't being helpful at all. They wouldn't even agree to call CX and ask whether CX could do anything.
Ultimately, I asked CX while I was on the phone with them regarding some other tickets with them. They said their position was they would protect anyone on a revenue ticket by moving them to the UL flight, but only revenue tickets. I think that's pretty lame, but then again I live in the US where the customer is king and we tend to have a much more expansive view of consumer rights than elsewhere (witness how it is virtually impossible for an airline to cancel even a $1 mistake fare that touches the US).
I guess I am left to just refund the cancelled CX tickets and use those Avios later. At least we are only talking about a $225x5 pax on UL. but having to deal with an economy flight of 3 hours 50 minutes. The biggest buzz kill is that it's in the middle of a trip where we're flying cushy F or J on all the other segments.