Joann -
Fortunately, you've got a few months before you travel. I'm not sure how relevant our experience this summer will be for your trip, as BA is under a lot of pressure to get the baggage situation sorted out.
Summer is the biggest crunch time for LHR. I would expect the volume of luggage for BA to handle is lower in November vs. June or July. They are also working with the government to ease the one bag carry-on rule, as that has added greatly to the number of BA checked bags. Hopefully, that will be changed by November, too.
FWIW, in general the airport situation in many cities this year has been the most difficult I've encountered since 9/11. Flying just isn't anywhere near as easy. The trickiest part of your itinerary is the three flights. No matter which carrier, more transfers are more opportunities (albeit slight) to have luggage delayed.
Cheers, Anne