Hi Peter,
I now read better your post.
I confirm that a simple stripe of paper between the transmitting IR-LED and the receiving fototransistor "solves the issue".

I consider this the best option at the moment; no sticky stuff around that get loose, no crack open the adapter.
I am setting up a test of a couple of hours (programmable power supply, reading from the multimeter) to verify the stability and reliability.
Thank you for the link to Kiriakos's post.
He is blaming Brymen for replacing the transmitting IR-LED in the multimeter; I am not 100% sure they did.
Indeed you reported that with an older USB adapter there are no issues at all; this demostrates that the IR-LED in the multimeter was not replaced.
I guess it is more Brymen was trying to cut costs getting rid of unneeded products, and someone declared the BM869s compatible with BC-86P.
This is not the case ... even during the software installation from the CD (you are requested to type in your multimeter model, so the right combination software/driver is choosen) you are alerted to be sure to have a BC-86x adapter.

I am in touch with the vendor and Brymen, anyway in my case Brymen still don't recognize their mistake.
At this point I am still not aware what resistor should be replaced in the multimeter and I have to admit I would prefer to work on the adapter instead.
Nevertheless, I'll wait for Brymen and live with what I have at the moment.
Luca