Chamonix to Florence by train?

It happens that trains are late on one leg and you miss the transfer.

I think we all know the SBB isn't going to let you down, but that first train is a French TER. I've looked at a lot of departure boards in France since May 1, and the TERs are sometimes late by more than a few minutes. If there's a departure from Chamonix an hour earlier, I'd consider taking it, assuming that missing the first connection would make you more than an hour late in reaching Florence. (I do not know whether that is the case.)

No issue other that seconding the advice above to make the initial departure a bit earlier. Obviously, the Martigny connection is the tightest one. While the French and Swiss tickets should work for any train on the route, tickets for the EuroCity and Eurostar Italia (a.k.a. Frecce) trains are sold for reserved dates, times, and seat assignments.

You might look at trains from Geneva Airport to Florence. You can take a shuttle to Geneva from Chamonix in less than an hour. You can depart at 11:50 and arrive at 18:59. Change at Brig and Milano.

Is it possible to take the cable car into Italy and get a train/bus from there?

I'm nearly certain someone posted about that possibility some time ago (or perhaps Rick mentions it in his guide book to France??). I imagine you'd be starting out on a bus, possibly connecting to a train depending on your ultimate destination.

Taking the Aguille du Midi and then the Mont Blanc Panoramic to Courmayeur is not a realistic option. It's an awkward route and the transportation is not as frequent. The Mont Blanc Panoramic could also be closed due to high winds or whatever.

I've travelled part of the route you listed above and although there are lots of changes, it's not difficult. Some of the scenery along the first part of the route is spectacular! It's unfortunate that there aren't more trains available on that route, but it appears that the train you mentioned arrives at Firenze SMN at 18:59 which is still quite a reasonable time. Check into your hotel and then stop for a fine meal in Florence! The train you chose seems to be the best one under the circumstances as the earlier 07:54 departure has one additional change and is two hours longer.

As suggested earlier, another option would be to take one of the many Shuttle services to the main station in Geneva, and connect with a train there. The Shuttle trip is about an hour as I recall. However if you used the 12:00 departure from Geneva, you'd still arrive in Florence at 18:59 on exactly the same train and the trip would only be slightly shorter, so I'm not sure there's any advantage to that.

A few additional points to mention. If you buy tickets for the TER locally, be sure to validate / composter before boarding the train on the day of travel. On the route you mentioned above, the latter two trains (EuroCity and Freccia) have compulsory seat reservations, which will be included with the tickets you buy. Are you planning to buy advance tickets on any of the trains?

Four connections would seem a recipe for disaster. Get to Geneva for a direct train to Milan at lunch time.

EC 39
Dep 13:39 GENEVE (Switzerland)
Arr 17:37 MILANO CENTRALE (Italy)
FR 9553
Dep 18:20 MILANO CENTRALE (Italy)
Arr 19:59 FIRENZE S.M.N. (Italy)

"Four connections would seem a recipe for disaster."

Actually, it's not that bad once you get the hang of it, but it is necessary to be pay attention and not stop for coffee at the transfer points. I've had as many as six changes in the past, which I tolerated because it was the best choice under the circumstances.

The Geneva route is also good but it's not going to be any quicker once the shuttle time is included.