I also had the same problem with a Core and a pair of BL 5000’s. The Core would turn them on but not power them down. They worked fine when connected to an Essence. It drove me insane that they wouldn’t turn off as they were installed in our bedroom and the display was always on generating an annoying amount of light.
I haven’t tried the B&O fix as I replaced the Passive with a BeoAmp2 after some renovations as it was a better fit for where it was being installed. I would have also had to wait months to get the cable made as we were in a covid lockdown at the time.
I have no reason to doubt B&O’s suggested fix as there was a lot of backwards and forwarding with them including sending them pictures of the installation. Like you, my dealer said that cable part 6271225 would work. Except it didn’t. I have 3 of the cables; all work fine with an Essence but when you connect the Core no go. I tried this on 3 different Passives and 2 different Cores all with the same result.
Perhaps you could contact a service centre and tell them what you’re trying to achieve and have them make the modified cable that they can test before selling it to you?
Peter