To close the thread...
On Friday I got the TMPS fitted to my winter rims. It cost more that what I thought as the fitting was extra (still much cheaper than doing it at BMW)
But it works again, so my number 1 button is again showing me the tyre pressure live, which is awesome
I guess though depending on how much a change of tyres cost you twice a year, it is more expensive to buy new rims and TPMS (atlhough they look cool
)