A little confused about paid upgrades on British. For context, I have an upcoming work trip, and can only book economy through our travel portal. Willing to pay (with cash or avios) for an upgrade to J.

I'm looking at what's available, and there's an itinerary that I think works for me BER to LHR, LHR to LAX. Looks like there's plenty of seats available in J according to expert flyer for the LHR to LAX route. I can book through British or American, but I'm assuming it's best to book direct with British.

Based on this thread, it seems like it might not be offered because I have a connection on the itinerary, and even if it does, I'll be booking through our corporate portal, so it might only be available 2-3 days before. Does that sound right?