Doug,
I know it easily possible to create a custom action that forces the selection of the Customer, however I am not aware that you can then reduce the project list dependant on that selection. If it was standard picklist options, then they can be dependant on each other, but I don't think a project list could be.
I'm guessing there might be a way to do this using some clever programming to filter the project list within a custom panel (We had to similar for Time Entry) but you would probably need to get the PS team involved. In my experience, most things are possible in some way or another, I'd suggest speaking to your Account Manager to see what the options are.