You can travel the same route using regional services; some train changes are required, though.
The Swiss Travel Pass is valid on regional services, too. You do not need to buy tickets - simply board the train and enjoy the ride. To get the itinerary, you have to work with VIA option. Via Chur, Via Disentis, Via Brig, as the timetable app tries to find the fastest connection which is via Zurich HB.
However, I suggest you that you should contact Glacier Express two or one day before departure. They might have some seats left from groups who cancelled the trip at short notice or groups with fewer members than planned and whose seats are again at disposal. Call the Glacier Express Rail Service, they are very helpful and speak fluently English: +41 81 288 65 65. Or go to the St. Moritz train station once you are on-site and ask the ticket clerk for available seats. You can still make a seat reservation with him/her if seats are left.