Cologne to Rome

Not have any relevant advice re the routing, but wondering about the one way drop fee from Germany to Italy not being a deterrent to this plan

Good thought, Joe, and the drop-off fee is a hefty $800, but we're doing it..

While in Luxembourg stop at Viaden on the German border, also take in the historic Roman city of Trier.

On your way to Colmar, stop and see Strasbourg, France.

Liechtenstein is not worth a diversion, but the scenery is nice in that part of Switzerland. Consider a visit to the Youngfrau and Interlakken.

Save at least three nights for Florence and five for Rome.

I think all rental cars in Germany have a downtown Umweltplakette sticker. But you'll need the Swiss toll Vignette, as well. I wouldn't do all this driving in Europe, or cover so much ground in a vacation. But you said you're experienced travelers, so (assuming you mean experienced in Europe) you must know what you are doing. I also don't care to change rooms every night, but that's personal.

There plenty of sights along the German-Swiss border, including various sorts of medieval towns, Roman monuments, specialized museums, and some river/lake scenery. I personally would be interested in Fondation Beyeler, the Vitra architecture campus in Weil am Rhein, Augusta Raurica, Stein am Rhein, Aarau, the Rhinefall. I was sorry to miss Le Corbusier's chapel at Ronchamp, France. You don't have time, I think, to make visits of this "density" for your entire route. It would be easy to spend a week just going from Cologne to Trier. Have you cruised the Middle Rhine already? Are you interested in Monschau, which almost needs a car?

Because September has Open Monument Day Weekend in Belgium and the Netherlands, I wonder if any other countries/big cities might have this?

Sounds fun! Perhaps my husband and I are more timid (we are also mid 50s) , but we tend to try to avoid the larger cities when we are driving. So my thought would be Eguisheim or Riquewihr in Alsace and Luzern instead of Zurich. I can't speak to Italy, I haven't been there yet :(

Caleb, why Zürich, why Liechtenstein? If you are driving through Switzerland, these are not the best places to visit.
As you have a car, choose a route which involves driving over the Alps by the passes, not through in tunnels. Watch some of these videos: https://www.youtube.com/results?search_query=grimsel+pass
or: https://www.youtube.com/results?search_query=nufenen+pass

And make sure all your hotels have parking, especially city centre ones, and are not in pedestrian-only areas (e.g. the "ZTL" in Florence).

Thanks all for the replies so far.

@geovagriffith,@Chris F: Liechtenstein is really just a check-box destination. We've spent time along the Bodensee and like that area, but thought Liechtenstein would be at least worth a drive-through. We'll be spending just over three weeks on this venture so have time for Florence and Rome, which we've been to many times before.

@Tim--good reminders on the car stickers we'll need. We've made many road trips through Europe--in 2015, for example, we put 2200 miles on a rental car in Spain--but completely understand the distaste of changing hotels ever night. We'll be holing up in a villa in Southern Tuscany for several nights to rest up from the road days. Monschau is a good addition--thanks.

@Chris--thanks for the vids on the passes--Grimsel pass looks amazing and is one we haven't crossed yet. I totally agree on avoiding tunnels. I actually hadn't thought about how we'll get from Liechtenstein to Lake Como so may need to rethink that route--and Grimsel looks so inviting we may scrap the Liechtenstein portion and keep to the west instead.

@Jules--Eguisheim and Riquewihr are great suggestions--thanks!

Planning is half the fun of the trip.