When I was working on my first E92 lease, I traded my VW Jetta GLI in at the time of contract negotiations and had a 2 month wait for my E92.
Now they didn't give me a car for 2 months, but they did give me a loaner for the last 2 weeks of the overall 8. So I rented a car for 6 weeks, and had the free loaner for the last two.
Not a perfect solution, but it was pretty nice of them I thought. You might see if they would consider a loaner for a portion of the time you are waiting for the ///M to arrive, but the entire time might be too much....
Current - 2014 F22 M235 - MT, CWP, Premium, Aluminum Hex/Black Gloss Trim.
Past BMWs: 2011 E82 135 - LBM, N55, DCT
2008 E82 135 - AW, N54, MT
2007 E92 328 - JB, N52, MT, ZSP (traded in for 135)
2007 E92 328 - JB, N52, MT (retired by a drunk driver)