It is worth noting that the car rental places near the St. Pierre des Corps TGV station close for lunch from 12-2PM, no delays, no exceptions. We had a nice lunch on the plaza, to await reopening. It's a tiny exaggeration, but a car is almost essential for any chateaux visits.
Amboise is an important location, but I note that you have a substantial list of chateaux, which might get longer, if you learn about others, drive by others, or learn of Son Et Lumiere or Candlelight (exterior) night events. Those tend to book up well in advance, as do the best guides, so I would not go without having booked what I want. (We never use private tour guides, so I can't offer actual advice on that.)
My solution (which is, I admit, a poor idea for some other tourists) was to cut out the chateaux to the east of Tours, and stay west of Tours. That was affected by our plans to continue West to Brittany and Normandy. But I was right in guessing that the daily travel time and traffic, plus parking and walking to the actual chateaux (especially the most popular ones) adds up to a lot of time. I recommend that you get a smaller car with at least "normal" ground clearance, since you may have to park in an overflow-parking meadow. It you like having a big or really fine dinner, you'd also want to sleep in reach of a restaurant zone. (We have our big meal at lunch, and might have snacks and wine at the hotel cafe for dinner.)
Do you know that TGV may have mandatory reservations for railpass holders? If you want to sit together, you certainly need to book online, even if there is a fee. You could get shut off a full train during high season if you don't book. With advance purchase discounts, there might be a few trips like this one where you might choose to omit using a railpass-day. Have you worked out all your railpass-days?
I am not up on current details, but SNCF now has two business names to sell premium and discount travel without contaminating one reputation with "discounting". (I mean, slightly like Groupon makes it look like the merchant doesn't undercut his/her own pricing ... )
It's hard to know what's available in Covid-Time, but we particularly enjoyed Villandry, tiny Château de la Bourdaisière (ambitious tomato and dahlia specialty gardens), Azay-le-Rideau, ruins of Chateau Chinon (also a good town to wander for dinner, down the elevator.) We found interiors less interesting, and we love garden visits, so we usually spent more time outside, or didn't even tour some interiors. Villandry gives out free vegetables from their gardens, in a wall-bin.