Paris-Lucerne-Venice

If I get this right, you plan on a one night stopover in Luzern on the way to Venice. I hate to say, but why not just fly from Paris to Venice? It is 5 hours by train from Paris to Luzern, followed by 6 hours by train to Venice, and that route uses the Gotthard Base Tunnel, so you will be traveling completely under those Alps. You could take a slower route mostly over the Alps, but now it is a 7 1/2 hour journey.

You have 8 days in London/Paris and 5 days in Italy. Fly and make it 6 days in Italy.

That has been a thought but might take an extra day for the trip through switzerland. I obviously don't want to spend all of my time in the tunnel!

Take the 7:18 am "Treno Gottardo" to Bellinzona and change to the EC train direct to Venice, getting you to Santa Lucia station at 2:42 pm. This route takes you mostly over the Alps with the older, shorter Gotthard Tunnel.

The day before, take the 7:21 am TGV from Paris Gare de Lyon to Basel and change to the next train to Luzern, arriving at 12:05 pm. That will give you a full afternoon and evening in Luzern.

That sounds doable.
I was again researching, and we can go Paris-Innsbruck.....8 hours; overnight, then Innsbruck to Venice. 5 hrs.

Or you could go Paris to Venice in under 10 hours through the French Alps.

Probably going to Chur overnight, then ride Bernina Express, then to Venice.
Option: go to Lucerne, ride Golden Pass then down to Venice. About the same train time. Any thoughts? Lakes look beautiful.
A little concerned about which would be best if the weather isn't great.

I gave you a scenic train ride my second post, taking 7 1/2 hours, with 2 changes.

Taking the Bernina Express from Chur will get you to Venice by 6:42 pm, taking 10 1/2 hours with 2 changes.

Taking the train from Luzern to Interlaken Ost, then Spiez and Brig will take 8 3/4 hours with 4 changes