Yes, they should check you through to the BA flight. It's not a guaranteed oneworld benefit anymore but there haven't been any reports here of it not happening and they've always done it for me, including very recently from Bangkok.

Worst case, I've done the QR to BA transfer landside at CDG before and it's pretty straightforward.

Sorry to hear you couldn't get switched to a UK destination. Yes they must have placed some sort of limit, by choice or algorithm, to maintain availability for other destinations. There must be very demand that week for some reason. It's a drag for you of course, but hopefully your short Parisian diversion isn't too painful. And next time if you are keen to include BA sectors you may be better booking through BA to benefit from UK 261 protection in both directions. Have a safe trip.