Driving Between Florence and Siena

I would pick up car at FLR and drive straight to Siena. Park the car and enjoy Siena today, get over jet lag, etc.

Next day head out to SG, and maybe Volterra returning to Siena for dinner-Siena is so enchanting in the evening.
Or spend am in Siena-afternoon in SG

( check closures in Siena Mon and tues-I am not sure)

Next day Tuesday
Finish any sightseeing in Siena then drive thru Val d’Orcia-stopping in towns of your choice-Montepulciano, Pienza, San Quirico, Montalcino
Evening in Siena

Next day Wednesday-drive Chianti Road to Florence
Return car there
No need to go to airport
Check open.closed hours of car agency-usually closed 1-4
Check market days
( wed might actually be market day in Greve-plan to have lunch there

Parking outside town walls is not expensive
A few euros usually
Be sure your hotel in Siena has easy to access parking.
I can think of a few really nice ones off hand

If you are going to rent a car rent it for as many days as you can and get all the use out of that rental.
All drivers must have and IDP
Make sure you have a designated driver if you are doing any wine tasting/drinking.
(We save our drinking for the evenings in town)

Here are directions for entering Florence for safe car return-Grazie to Roberto
https://community.ricksteves.com/travel-forum/italy/picking-up-a-car-in-florence-to-drive-thru-tuscany

Perhaps from the airport, train to Siena & pick up car there. Saves on parking for a day (or two) as well as cost of rental. When arriving at Florence, drop car off and do daily rental if needed.

Warning: Be very careful of ZTL's (or LZT's if you prefer). https://en.wikipedia.org/wiki/Limited_traffic_zone

SR222 is quite curvy and somewhat tiring to drive; after flying I would drive the highway to Siena. The highway itself is a bit demanding to drive, as lanes are narrow.

I wouldn't drive the SR222 after an overnight flight, but maybe you are better able to sleep on a plane than I am. The road is a two lane highway that is not only curvy, but also narrow and with no shoulders on the sides. So you have to be alert.
The freeway is better.

We're spending the previous day/night in Copenhagen, so we won't be fully jet-lagged upon arrival a FLR. I'm more concerned about the left luggage in the trunk (if we stop along the way) than being fatigued.

It seems like if we take the freeway directly to Siena (or back to Florence), we'll be somewhat inefficient because we'll have to use part of another day to visit Chianti or San Gimi (unless we just skip them entirely). Visiting them en route seems better ... in theory. The other problem with getting to Siena (or back to Florence) too quickly is that we might not be able to check-in yet, since we'll likely be in Airbnbs instead of hotels.

Driving on the rural roads, including the very pretty Chiantigiana (SR222), was an absolute pleasure for us. Driving on the Autostrada ... not so much.
Consider taking the bus or the train to Siena upon arrival in Florence and collecting your car after arrival. There are a number of rental car outlets near the train station, including a Hertz concession within walking distance a couple of blocks away, but you'll need to verify Sunday operating hours - many are either closed or operate on very restrictive schedules on Sundays and holidays. Could return the car in Florence which would allow you to meander up the SR222 on your last day.
Know too that there's cheap underground parking in front of the train station (2 Euro per day), from where it's a series of escalators to get up into the town or (if encumbered with luggage) a taxi to the vicinity of the Campo costs about 12 Euro. The lot was particularly convenient for us during our last visit, and there always seemed to be plenty of availability. Others here have cautioned about it being full on festival days so be aware of that.

Since jetlag will not be an issue in your case then it shouldn't be a problem to take the SR222.

There are two ways to join the SR222 coming from the airport

1. From the start of the SR222 via Grassina from the Firenze Sud A1 exit
   https://maps.app.goo.gl/yMLRacG4vrEsGavr5

2. From Greve in Chianti, via the Freeway to Siena, then Ferrone and Passo dei Pecorai and Greve.
   https://maps.app.goo.gl/TRKfYyQijPi989oK6

The second option is easier and I like that stretch since it's full of pine trees near the Pass. But if you want to stop by the Ristorante Padellina in Strada, famous for his Florentine Steak, then you should take no. 1.

I wouldn't worry about the luggage being in danger in those villages along the SR222. But don't leave major valuable items (like phones or computers) just in case. Take those with you.

Thank you all for such helpful feedback. A couple more thoughts based on the input. In all cases, I'll compare fees first.

1) Train/bus to Siena on arrival day: This seems more complicated than renting a car from FLR. I know we'll have to wait for the FLR rental shuttle (up to 20 mins), but T2 --> SMN --> Siena-bound, Sunday train or bus could result in wasted time (or stressful hurrying) with luggage. If anything, we could consider the train/bus back to Florence, instead of 222 or San Gimi on the way back.

2) Back to Florence mid-week: We'll stay in Oltrarno. If we drive back from Siena, should we drop at the airport or in town? I've read Robert's great advice here, but I see some agencies have recently moved their offices near SMN, which looks "deeper" into Florence than Borgo Ognissanti. A lot could go wrong between bus lanes, aggressive Vespas, major roundabouts, missed turns into ZTLs, etc. How much time would we add by dropping at FLR, assuming it would be less stressful? (And if we do take the train/bus back to Florence, I assume we'd cab to Oltrarno with four people and luggage).

1) That's too much hassle since you plan to rent a car anyhow. I never had to wait for the rental shuttle that long, at most 10 min. The ride is maybe 3 minutes. It's actually walking distance, but it's not walkable road (no sidewalk and a freeway to cross) so don't attempt to walk it in spite of the proximity. Take the shuttle, rent a car and drive to Siena. If you want to have a leisurely drive on the SR222 take it. It's a longer drive, especially because I'm sure you'll want to make stops along the way for photos, lunch, whatever, but the drive itself is less than one hour longer than the freeway.

2) Whether you want to return the car at the airport or in town is up to you and how comfortable you feel driving in city streets. Obviously returning in town will save you some time (and a few euro of taxi fare) since the airport is on the opposite side of the city compared to where you are coming from. Only Hertz has moved their office to Via Alamanni (next to the station). All others are still on Borgo Ognissanti and the return is at the Interpark Europa Garage on that street. I don't know if Hertz has the return in the garage under their new office on via Alamanni. For sure to return on Via Alamanni it is impossible to avoid the camera because you will necessarily have to drive the last 100 m. on the tramway lane, therefore if the return is there, they must put your car's license plate in the City White List online to avoid the issuance of a ticket. I've given instructions on how to return the cars at all Florence locations (airport, Borgo Ognissanti, Via Alamanni) below:
https://community.ricksteves.com/travel-forum/italy/dropping-off-hire-car-to-hertz-in-florence
https://community.ricksteves.com/travel-forum/italy/dropping-rental-car-off-in-florence
https://community.ricksteves.com/travel-forum/italy/florence-car-rental-zlt-zone

From where you drop off the car you will take a taxi to your hotel. If you return it at the airport I would take a taxi directly from the airport rental center, I wouldn't bother to take the shuttle back to the terminal, then the tramway to the station and then the taxi to your hotel. The taxi fare will be around 25-30 euro, including the extra charge of 1€ per bag. The transit+taxi combination will take longer and in the end you'll save no more than 5-10 euro.

Hi, one follow-up question. I read that Sam Gimi is especially busy on Sundays, since it's also popular with locals. Should I still expect that in mid-October? If so, that would be another reason to drive south (Sunday) through Chianti, and then back north (Wednesday) via San Gimi, which I assume mid-week would be quieter. I was starting to favor San Gimi / Autostrada on arrival day (Sun), so that on Wed, we could make a reservation for a nice lunch in Chianti, and not have to stress about getting there on-time the day we land.