Kathy and Craig beat me to it. I was busy looking up other options before posting about Mac’s Adventures. They specialize in self-guided hikes, and have several options for the Tour du Mont Blanc.
https://www.macsadventure.com/us/tour-listing/?rgid=&lcntyp=R&mactids=1&sactids=5,6,8,17,18,19,20,21&rbdid=418
I suggest you look at the “short break” (5 days/4nights) and the “Highlights” 8 days/7 nights). The difference is that the short break walks from Les Houches to Courmayeur in Italy, 3 days of actual walking on the trail, 10-12 miles a day; while the Highlights covers selected portions of the whole route around the mountain. I believe the “short break” tour has 3 nights in inns and one night in a rifugio.
I think I saw previously that you are interested in a 5-day trek, and I immediately thought of Les Houches to Courmayeur because it would be the easiest in terms of transport to and from the start and finish. Coincidentally, this the same section that Mac’s offers. And apparently pretty close to what Rick did on his first TMB trek—-the one in the French Alps show.
I actually do not recall a lot of the scenery on the trek we did, in part because our Day 2 was very rainy, with limited visibility. But I do remember Day 3 (the day we ended at Courmayeur) being beautiful, with a hanging glacier that we passed, and a traverse of a meadow filled with more wildflowers than I have ever seen in the Alps (in Switzerland it seems the cows graze most of them away).
The other day I remember is the last day, hiking back to Chamonix from Argentine (actually from a trailhead at Le Col de Montets). It was a beautiful sunny day and we hiked the Grand Balcony route, with views across the valley to the whole Mont Blanc array of peaks (Aiguille du Midi, etc.). You can see the view in this photo on the MT Sobek TMB page (this is the company we went with for the TMB):
https://www.mtsobek.com/trips/europe/the-alps/alps-tour-du-mont-blanc-express-hiking/
You could easily add that hike to your trip either before or after the “short break” self-guided option with Mac’s Adventures buy spending an extra night or two in or near Chamonix. Take the bus to Argentiere and find a way to the Col des Montets trailhead (taxi?). And hike the Grand Balcon du Sud back to the La Flegere lift (about 10 miles). Ride the lift down to Les Praz de Chamonix, a 20-minute walk from Chamonix. There is a nice little hotel there if you don’t care to spend more time in Chamonix itself, and the train stops there (or did when we stayed there years ago).
I looked at other companies that offer a self-guided TMB, Such as Alpenwild, Ryder-Walker, and Alpine Hikers, but they all offer only the full deal in 10-13 days, charging $2875-$3190. I also looked at Distant journeys, the company my friend used for her self-guided TMB, but they do not include luggage transport. And I don’t know that they offer a shorter trek than the whole circuit.
Is it too late to book for 2022? You won’t know until you ask. But I did notice when I was looking at the Alpenwild website that their guided TMB tours are almost all sold out for 2022. This could mean that the lodging (huts and inns) are getting booked up, so you shouldn’t wait too long before booking.