Good afternoon,
I am a SQL Server developer/DBA with over twenty years of experience on SQL Server and the Microsoft stack. There are many possible reasons why an MDX query performs poorly, not the least of which could be how you have the data partitioned as you suspect. It will probably take longer than an hour to diagnose, however, as I'll need to gain an understanding of the data before I can tell you how to correct the cube definition and/or MDX query. I am in the eastern US time zone and I have time Monday morning to help you through this issue should you choose me for this project.
I look forward to working with you.
Thank you,
Rodney Kendall