Zugspitze

I would take the train to Garmisch-Partenkirchen. Then transfer to the train that goes to Zugspitze at the train station.

https://www.youtube.com/watch?v=S28aHwId0CA

Take the S-Bahn to the main station and from there the train to Garmisch. Buy a "Regio Ticket Werdenfels", with which you can travel at any time (€31 for two, valid for multiple journeys same day). Don't book in advance, because if the weather is bad on the day of travel, you can't cancel it. The best thing is to download the DB app on your cellphone and book it there at short notice. Or at a vending machine at the station. If the weather prospects are good, I would go as early as possible, because in the mountains the weather often changes in the afternoon. The Zugspitzbahn station in Garmisch is right next to the DB station. You go to Eibsee with the rack railroad, and from there you have the choice: either continue with the rack railroad or with the cable car.

Here's some cloud cover info for Garmisch-Partenkirchen. Needless to say, check the weather beforehand.
https://weatherspark.com/s/70225/2/Average-Fall-Weather-in-Garmisch-Partenkirchen-Germany#Figures-CloudCover

We moved hotel from Garmisch to Partenkirchen as it was more charming. Try to see both of these cities and Zugpsitze too.

If you are traveling by rental car, I would look for an alternative--the Grossglockner High Alpine Highway. It goes over Austria's highest mountain peak. It's simply the most beautiful mountain scenery I've ever seen.

You enter the road just south of Zell-am-See, Austria which is south of Salzburg and it ends down on the Italian border at Lienz

https://en.wikipedia.org/wiki/Grossglockner_High_Alpine_Road

https://www.grossglockner.at/gg/en/index

Take the S-Bahn to the main station and from there the train to Garmisch.
Buy a "Regio Ticket Werdenfels", with which you can travel at any time

Note: Don't wait until you are at the Hbf to buy the Werdenfels Ticket. Buy it at Marienplatz, before heading to the Hbf, or with the App before you start. Then it will cover you on the S-Bahn from Marienplatz to the Hbf as well as on the train to GaP.

You say there are six of you, but the maximum number of adults over 14 on a Werdenfels Ticket is 5. However, children from 6 to 14 (up to 3 of them) travel free on the Ticket And children under 6 are always free on German Rail trains. Hopefully, one in your party is under 15.

The basic Werdenfels Ticket for the first person is 23€. Each additional adult over 14 is another 8€.

So, if only five in your party are over 14, the Ticket would cost 55€ (23€ plus 4 x 8€) and the under-15 child would be free.

Or, if your family is 2 adults and four children under 15, at least one of the children would have to be under 6 and free, and for the other five, the ticket would cost 23€. If everyone is over 5, one of the 6-14 children would have to be paid for as an adult (8€ more).

When you are standing in front of the GaP station,looking out at the tracks, the Zugspitzebahn Bhf will be to your left and there should be signage showing you the way.

"the Grossglockner High Alpine Highway"

... will close down in the first week of November.

You go to Eibsee with the rack railroad, and from there you have the
choice: either continue with the rack railroad or with the cable car.

Actually, unless things have changed since I did it in 1988, you go from the Zugspitzebahn Bhf in GaP on a non-rack train to Grainau, where you transfer to the rack (Zahnradbahn) train which goes to Eibsee, then through the mountain to a saddle on the back side, and from there via a lift (chair? Gondola?) the rest of the way to the summit. At Eibsee, you can get off and save time by taking the cable car to the summit.

I'm mentioning the change from the non-rack train to the rack train in Grainau so you won't wonder what's going on when you get there.

Being from Colorado, I wasn't that impressed with the 9718 ft Zugspitze. It's not as high as the parking lot at the base of Loveland Ski area, where I used to ski at over 12,000 ft. I've taken the rack rail train to the top of Pikes Peak (14,110) and driven to the parking lot (14,130 ft), below the summit of Mt Evans (14,264 ft). But then, you're from Florida, and the Zugspitze is 9373 ft higher than anything there.

Read and weep.

https://www.denverpost.com/2022/10/03/silverton-mountain-first-skiers-snow-dusting-2022/

"the Grossglockner High Alpine Highway"
... will close down in the first week of November.

Too bad the OP will miss this. The Großglockner Hochalpenstraße is a fantastic drive.

There is also a website (sorry don't have it handy) with webcams to check visibility before you head up. G-P can be interesting to visit.

https://www.foto-webcam.eu/webcam/zugspitze/
https://www.foto-webcam.eu/webcam/zugspitze-sued/

the week of 11/20

Important: According to the Zugspitzbahn website, all traffic (train and cable car) to the Zugspitze will be interrupted from November 7 to 11 and from Nov 28 to 1th of Dec for annual maintenance work. In addition, the cable car will be out of service from Nov 14 to Nov 25.

Actually, unless things have changed since I did it in 1988, you go from the Zugspitzebahn Bhf in GaP on a non-rack train to Grainau, where you transfer to the rack (Zahnradbahn) train

This has changed with the acquisition of new trains in 2016. In regular service, the trains now run from Garmisch to the Zugspitzplatt. Only at peak times (July/August, January/February) are the old trains still in service.