Some control modules have many more part number versions than what is listed in RealOEM and the likes. I noticed this when looking for LM2s for the e63s and also the Bluetooth module was an even bigger nightmare part number wise.
I believe that the different part numbers actually mean that there is a revised version of the software on the module. I think you have probably called it correctly, any Mini ASC unit from a car with ASC will be fine.
There's a guy I use for work on my Mini here in Cork, Ger O'Leary has a few of them scrapped (I think). He would be worth a call, he has specialised in Minis for years. If has one that suits and a price that works for you I could collect it from him tomorrow/Friday. I'm traveling to Dublin Saturday so I could drop it up for you. He is only over the road from my place of work.