Ok, thanks all.
I will put more pressure on my Sales Consultant (or whatever they call themselves) and ask to speak to the service department if needed. He also asked me to keep him updated because he has another client in the same situation where they told him they would not do it. Seems like the other guy doesn't have the same great resources that I have (ie: this forum). Thanks again!
As part of the delivery due sometime this winter, they offered to install whatever winter sets I found on my own. I would much prefer to pick up my brand new MINI already equipped with proper winter tires than have to deal with this on my own in under seven days. (for the curious, this is the delay we get here, where winter tires are mandatory during winter)