There's a travel vlogger I like to watch named Steve Marsh, he recently did a daytrip to Rocher de Naye from Montreux. I didn't realize the train left from Montreux station, I thought you caught it down near the Castle Chillon. It's another of those little cog railways with great views, and in March he had the place to himself.
Steve also stayed at the appropriately named Freddie Mercury hotel, if you are into trains you'll want to check this place out since it is literally right next to the tracks - if the windows of the rooms open you could reach out and touch the passing trains.