The best solution depends on your analytic needs and on the meaning of those Xref tables, but in any case, you are going to de-normalize and include more attributes in your Fact Table. For example:
Left-Join Market-To-Project Xref into the Fact and eliminate the Xref
Left-Join Territory-to-Customer into the Fact and eliminate the second Xref.
Now you need to take care of the third Xref... I'm not quite sure what's the meaning of it, so I'll leave it up to you to decide... It looks like knowing the Product and the Customer from the Fact Table, you can determine the Market and the Territory from the two Xref tables. What's the third Xref table for??? When you answer this question, you'll know how to properly model it...