Too close a call. If you go to the wrong platform as I did once, you'll be out of luck.

Since I found this brought back up again... I'll add one more question. Are there ATM's at the smaller Swiss town train stations? Particularly, Stein-am-Rhein?

I've seen a lot of Swiss stations but don't remeber ATMs at smaller ones, may be but there will be one very nearby - they're all over the place.

Just be ready to jump and run when the train stops. :) Usually the departing trains will wait on the arriving ones. They know people are making the connection and will wait. The only time this didn't work for us was when we were on a Deutschebahn train from Germany to Austria and the Austrian train didn't wait when we were a few minutes late. That's only once in 6 years of much train travel in central Europe. So don't worry about it but don't piddle around while changing trains! :)