I've had a look at the options in piviots and straight tables. You cannot set the label dynamically so setting the label to CustomerId on the ordered dimension is out.
Aggregating the measure also doesn't cause the dimension to split out along the lines you need either.
There is no way to hide dimension although you can order the least import ones at the end of your table.
One way you might want is to use a master items drill down so it starts at Customer then clicking on it gives you the detail at order level but again doesn't satisfy your exact brief.
As you allude to its not an obvious request to have to satisfy.