Munich - Bernina Express - Varenna

The problem you are encountering is you are trying to second guess the trains, and forcing reality to fit into your guess.
If you want to get a train from A to B, you look up trains from A to B, and let the timetable website tell you which places to change trains.
You also need to consult a map, preferably a rail map, not a road map. For example: https://www.sbb.ch/content/dam/sbb/de/pdf/freizeit-ferien/ferien-kurztrips-schweiz/internationale-gaeste/sts-geltungsbereich_en.pdf

First, Monday 16th October you want to get From Munch to Luzern. Look that up on bahn.de, and it will tell you. The answer is the 07:17, change at Zürich HB for one of the half-hourly trains to Luzern.
There is no point in staying in Zürich, just get a quick train to Luzern.

I then looked up "Muottas Muragl", I had never heard of it: https://en.wikipedia.org/wiki/Muottas_Muragl
So, it is part way along the Bernina pass railway.

Question: In which case, why are you going to Luzern, it is a double-back to get to Chur (the start of the Bernina railway)? Why not go direct from Munich to Chur, overnight there and you are in the correct place for the Bernina Railway the next morning?

That makes 3 rail trips:
1) Munich to Chur (no need to go via Zürich or Luzern)
2) Chur to Muottas Muragl
3) Muottas Muragl (via Tirano) to Varenna

You can look up all 3 on the SBB (Swiss Federal Railways) website: https://www.sbb.ch/en/
Varenna has a station (called Varenna-Esino), no need for a bus.

P.S. you could even go Munich to Muottas Muragl on the 16th and have your 2 nights there.
I looked it up on https://www.sbb.ch/en/ Depart München HBF 07:17, arrive Muottas Muragl (summit station) 14:25

Have a look to the map on Google maps:

There is a sort of railway triangle between Pontresina, St. Moritz and Samedan. On the line between Samedan and St. Moritz the Punt Muragl railway stop is very near the base station of the funicular to Muottas Muragl.

Also the branch between St. Moritz and Pontresina has a station named Punt Muragl Staz (I guess Staz is for Staziun). This stop should be only few minutes walking from the base station, including crossing a bridge over river Flaz.

Please note that we are talking about two different stations, both very very little, on two different branches. When you come down from the hotel, the Bernina line has the stop on the Punt Muragl Staz, but you may well take a connecting train to Pontresina from the closest Punt Muragl station, your final destination is Tirano in Italy.

In Tirano you exit from the Swiss station, you cross the piazza, buy a ticket to Varenna at the Italian station and board a direct train.

Now, how do you get there? This is the difficult part of the reply. Likely through Chur and Samedan. But I wonder if you really want to spend your time and money going to Luzern, that is nowhere close to Punt Muragl. But even the shortest possible itinerary, say with an overnight in Chur, is quite complicated from Munich, as there is no direct line.

You may have a look also to https://www.youtube.com/watch?v=62uXj1ssR0Y

When the video of the ascent is over, there is a short sequence where you can see the access to the base station of the funicular. At 9:57 the train from Samedan is leaving the Punt Muragl station to Pontresina. A white bridge crosses the river, there are two ramps and on the very top of the screen the Punt Muragl Staz stop. At 10:07 as the train crosses the river on the iron bridge, it is more clear that on the background there is a second railway line. Cars are parked by the base station of the funicular.

(For railway buffs: this arrangement is necessary as the Bernina line (St. Moritz-Tirano) has a different electric system that the main Rhaetische Bahn network; so a Pontresina-Samedan shortcut was built, but had to be completely separate from the Bernina line. Travelers to/from Samedan usually change in Pontresina, but there are a few through trains - engines may be changed in Pontresina through a commutable overhead line over one track.)

In fact, if my ancient grey cells remember correctly, there are actually three different electrical systems, with three different voltages (I think the one nearest Italy is actually DC) between Chur and Tirano.

(removing anorak and binoculars)

Bernina railway - 1000 V DC
Rhaetische Bahn core network - 11 kV 16.7 Hz AC
The Arosa-Chur line was 2400 V DC till 1997, but has been converted to 11 kV AC as the rest of the network.

Both St. Moritz and Pontresina station have both voltages; in St. Moritz there are two separate areas of the station, connected by a short link with no overhead wire. In Pontresina there are two separate areas as well but track 3 has commutable voltage on the overhead wire for through trains from Tirano direction Chur.

Thank you all for your help!
Chris -- The railway map was a huge help! I didn't realize Luzern was so far out of the way. It had made more sense when we planned to stay there 2 nights. Now it seems more logical to go Munich to Chur first day, Chur to Muottas Muragl on the second, then on to Varenna the third day. Going Munich all the way to Muottas Muragl is still a possibility, though it would be a long train ride with multiple changes, i.e., more chances for a misstep.
I'll go back and read the Man in Seat 61 again, but should I go ahead and buy tickets as soon as I decide?

If taking the 7:17 EC train from Munich, it is only one more hour to Punt Muragl than to Luzern. The first change is 29 minutes in St Margarethan, and once you get to Chur, even if you were to miss a connection, the next train will be 1 hour later. The Murottas Muragel Funivia is just 2 miles from Samedan station, and if you missed the connection there, you could take a bus or a taxi if you didn't want to wait for the next train. Looks like an amazing mountaintop hotel

My heartfelt thanks to all of you who posted and helped me with my trip! Thanks to your detailed directions, all went perfectly. We took the Alex train from Munich, stopped in Lindau for lunch, made the next two connections easily and stayed overnight in Chur. The helpful RBB office there figured out our schedule and printed all our tickets for the next two days. We opted not to do the official BEX, but sprang for first class tickets on one of the red trains doing the same route, and on the first day had an entire compartment to ourselves.

We stayed overnight at the Muottas Muragl, above the treelike at the top of the funicular, which was one of the highlights of our trip. If you're OK hiking at 8000 ft, there are multiple trails, some that looked fairly level. But the view from the wide west facing deck is amazing, especially being buzzed by the hang-gliders. I want to come back here in winter and see it in the snow!

On the next morning we went back down by funicular to the tiny station Punt Muragl, pushed the button, and the train stopped for us. This mid morning train had lots of hikers, but we got seats together soon after a few got off. Another beautiful ride to Tirano where we changed to an Italian train to Varenna. Lucky October weather and a great trip. Thanks again for all your help!!