That's a very popular climb and not surprised at the chokepoints. I assume hut reservations made over a year in advance? hopefully not first come, first served?
I just dug through some October 2017 pics, we took the Gornergrat railway up to the observatory (10,285 feet) for sunrise pics, then hiked down towards Zermatt stopping in Sunnegga (sp?) for a beer of course. Not a SUMMIT! but a nice hike, the change of scenery is incredible working your way down, went from below freezing to maybe 65f? awesome