The Brig route is what came up as the best when I put in Lauterbrunnen to Andermatt—-I did not try to favor going to Brig or get you to the Glacier Express specifically. I don’t understand why you want to avoid it.
But if you want to go another way, you can make SBB show you other routes by putting in an intermediate stop. Here is the map of the Swiss rail system so you see what might work:
https://cdn-doc.myswissalps.com/docs/default-source/rail-network-maps/swisstravelpass.pdf?sfvrsn=7788603a_52
Putting in Luzern (the logical choice) as an intermediate stop between Lauterbrunnen and Andermatt, you will see routes that get you to Andermatt in a minimum time of 4h 34 min, with 3 or 4 changes: Interlaken Öst, Luzern, and Göschenen at a minimum; sometimes Arth-Goldau as well. Going via Göschenen routes you on the Gotthard Pass route, avoid the faster Gotthard Basistunnel which goes under the Alps, bypassing Andermatt altogether.
Just remember to check the Glacier Express schedule to see what time it departs Andermatt so you don’t miss it—-unless you are content with a regional train. In September there should be 2 GE trains a day, departing Andermatt eastbound at 10:54 and 11:54.
Starting at Montreux, the fasted time to Andermatt is 3hr 3 min, with a single change at Brig. This one departs Montreux at 8:42, arriving at Brig at 10:02, giving you 16 minutes to catch the Glacier Express departing at 10:18. This is the same train you would meet at Andermatt if you skip Brig and go the other way. In summer it is the later GE, listed on the schedule as PE 902. Reservations are required on this train, but not on the regional,trains.
If you are doing this and the Glacier Express portion to St. Moritz all in one day, I suggest you keep the travel time to meet the Glacier Express to a minimum. Or consider riding a regular regional train on the route ( same tracks, same scenery) as Nigel suggested. If you end at Chur and overnight there, that will shorten the day’s journey and you can start your Bernina Express trip the next day.
Note that the famed Landwasser viaduct is on the section between Thusis and St. Moritz, so you will see it on either from the Glacier Express or the Bernina Express. We like sitting toward the back of the train so you can see the front of the train rounding the curve ahead of you. (Weride the regional train on the Bernina route, so I don’t know if this works on the Bernina Express panoramic cars.)
https://www.myswitzerland.com/en-us/experiences/rhaetian-railways-landwasser-viaduct/