Andy - we have a v early (April 2012) M3W and we therefore presume it has the original the 12 pin TSM which takes an input from the speed sensor. Not sure whether your car tested without the pull up resistor has the 12 pin TSM or the later/more common 18 pin version.....
Is there any indication from your interactions with Alister W that the pull up resistor might have been needed for this early TSM but perhaps not required (but left in) for the later 18pin TSM???
If required, we are happy to be guinea pigs on this with the one we have ordered from you (if of course you have not already tried without the pull up resistor on both types of TSM....)
Yes, my M3W is only a little younger than yours (June 2012) so has the 12-pin TSM. It originally had the sensor with pull-up resistor but also seems to work fine with the later type that doesn't have the resistor. I'm not sure when MMC started to use the sensor sans resistor as standard, but it was certainly before late 2019 when the 18-pin TSM would have been fitted.
I did check with Alister and he confirmed that the 18-pin TSM does not include a pull-up resistor.
I'll send you a PM about what sensor I send you!