Hi there - we've run into this problem and we solved it by installing really neat third party software called www.trayselector.com. It allows you to add toolbar buttons to Word and setup each button to print to a specific tray printer combination.
It works really well and is a very inexpensive solution to the problem which saves a lot of time and paper which is wasted by users sending print jobs to the wrong paper trays and printers. Cuts down on a lot of support costs and frustration too.
Hope that helps