Alright I took some notes. In last week or so I've taken some more free biz Wifi-Enabled planes, as follows:

B-HNE (773): free Wifi working, enabled on ground
B-LBE (33P): free Wifi working, didn't use until airborne
B-LQD (35G): free Wifi working, wifi off until 10 mins after takeoff and turned off again before landing.

I think the Wifi working thing is just a crew toggle?

Note my comments are about J class. I have not yet been on any plane where there was an option for DMs. It's just the box on the Wifi login page that says "Business Class", the far left free option and you put in your last name and seat#.