Germany to Switzerland to Italy

So, you only have 2 nights/1 full day in Switzerland? Any way to add some more time here? If not, I guess Lucerne for your one day.

Have you looked into Berner Oberland instead? It's part of RS Best of Europe tours.

I would love to add a few more days but--I use miles to book business class and availability is very limited. Originally booked directly into Milan, going from there to Bellagio, and working our way down through various parts of Italy. I currently have better pricing booked into FRA. I really don't want to reconfigure a month long trip so at this time, this little snippet of time is all we have. I will continue to watch for an option to add on a few days but if not, I would like to just get a little taste of Switzerland.

I am thinking that Berner Oberland would require more time--and we obviously don't have much to spare on this trip.

Thoughts on the best way to get from Lucerne to Bellagio. I've looked at Rome 2 Rio and The Man in Seat 61 but am still a little confused. I've read about the Bernina Express but just not sure if that is the best option for the short amount of time that we have. I am trying to understand the best balance of scenery, cost, and convenience. Since we have a fairly extensive itinerary during our time in Italy, I don't want to make this too complicated.

From Luzern, I would take the Gotthard Panorama Express, which runs until the third week of October or so.
It combines a boat ride on the lake with a scenic train ride to Lugano over the old Gotthard railway.
From Lugano to Bellagio, you can either take the bus to Menaggio and the ferry, or the train to Como S Giovanni and buses/ferry.
The Bernina railway is beautiful but takes too long from Luzern.

You can take the Gotthard Express, or you can do the exact same route on regular boats and trains all year long. That's what we did when we left Luzern for Bellagio (although we stopped for a few days in Ticino). Doing this gave us more flexibility, and we also rode on a much nicer ferry across Lake Luzern. Either way, taking the actual Gotthard Express, or following the route, it's a scenic way to go.

youtube is full of vlogger videos about the Bernina Express if that would help make up your mind, I assume there are Gotthard videos as well.

What a shame that your time in CH is so limited, maybe you just want to bite the bullet and skip it? Perhaps you could do an overnight train to save some time?