Ok- so outside Greve in Chianti.
I am curious as to why you are staying in 3 locations all about 30 min drive from each other. You could easily visit Siena from Greve, Greve from Florence, Siena from Florence, etc.
I'd branch out a bit more and see more of the Tuscany area. Somewhere in Val D'Orcia like Pienza or Montepulciano.
I hope you are not planning to have a car in Florence- you won't want or need. Will just be a big headache.
Flight at noon is not going to US so arriving at FLR by 10 should be fine- I'd still want to be staying pretty close by. Stuff happens.
Are any of your lodgings changeable?
If so
Fly into Florence
Pick up car
Drive to furthest south location- Pienza or Montepulciano 4 nights
Then to Siena I guess or just day trip Siena from Greve
Greve 4
Lucca? 4
Drop car in Lucca- train to Florence 4 nights
Fly home
You might consider some time in Umbria rather than more Tuscany- Assisi, Spello, etc. As long as you have the car!