I'm 99% convinces the rearrangement of these deck chairs for the mid-week meeting were simply to get the name "school" out of the program, thus an end-around any governmental authority.
I think you've got something there Lostgeneration. There was only a matter of several weeks between the new Jan 2016 arrangement being announced (no more TMS - at least in name) when items about illegal/unregistered schooling started appearing in UK news items. These items mostly referred to Madrasses and Jewish schools - with OfSTED (government schools inspectorate) undertaking investigations. So I'm guessing that someone in JW HQ received advanced legal advice and they made the changes accordingly. So the reasons given by the WTBTS / GBoJW may well be false, as they were for the "simplified arrangement" years ago, and for other changes embarked upon more recently.