Hi Nini - you have perhaps three days in the vicinity of Luzern. Possibly, day 2, as well as day 4 and 5. Just to Luzern itself is at a minimum, 2 hours and 9 minutes on one route through Thalwil departing Chur at xx16, and up to 2 hours 49 minutes via Zürich on the routes departing at xx09, which could be even longer if you do not choose the bus for the stretch from Zürich to Luzern....that stretch is nice train ride.....
You can maximize your days by staying overnight in that vicinity.
Also, there will be a fair amount of jet lag distributed among your fellow travelers.
That makes me think that you will sleep through the Bernina Express Route.
I am definitely puzzled why you have not chosen time in the Engadine....either the high-priced end, at St. Moritz, which you will pass very close to on the Bernian Route, or at the other end, which I happen to like a lot....Scuol, Guarda, maybe Ardez.
Obviously, all such choices are personal.
Finally, although I have not been to Liechtenstein, except when passing though on the way to Austria, I'm not clear on what the appeal is for a tourist.
Food- in Chur and the Graubünden...Gerstensuppe, pizzocheri and capuns. We liked the soup and found the pizzocheri to be bland for our tastes. Also, but perhaps to a lesser degree, capuns.
And, from the Graubünden, Bündnerfleisch, of course.
A local food group due for serious consideration is the really excellent red wines from the Bündner Herrschaft... Maienfeld, Jenins, Fläsch, Malans, and Zizers, all near Chur. Some have developed an reputation among connoisseurs, and command excessive prices...wines of Gantenbein from Fläsch, and of Christoph Jenny from Jenins. I have developed a taste for somewhat less expensive reds wines from the family of Hansrüedi Adank in Fläsch.