Revisiting the Swiss Railroad Timetables (they changed the schedule back on Dec 12, 2110), connecting in Visp to Zermatt seems to be the choke point.
There are multiple train connections from Sargans to Zurich to Visp. From Visp to Zermatt, trains run about once an hour. So teams could possible gain an hour advantage catching the right train. If they happen to catch the 1510 train, they would actually gain a 1.5 hour advantage over the next train.
Any team that could catch the EC8 train in Sargans at 1139 would enjoy that 1.5 hour head start and arrive in Zermatt @ 1614. Any teams on trains from Sargans after that departure will arrive in Zermat at 1754.