For that kind of money you could just hire a driver for the day. You can try to select some wineries in advance or ask the driver's company for places they usually go to and they can plan out a good route to cover the wineries you are interested in.
Montalcino would meet your requirement for very good wine in a short period of time as it is very compact with some very good wines so you could do 3, maybe more if you only want to taste and not tour. However it takes a couple of hours to drive from Florence to Montalcino. You might want to consider staying there overnight and then you could do 2 days of tasting which would cover a lot of wineries. It is useful to email the wineries in advance.
Chianti is closer to Florence from a driving perspective.
I have a done a couple of tours on different trips to Florence. I have a done a wine tour with 8 people which included 2 wineries and lunch at Dario Cecchini's place in Panzano (Since you are also foodies). See this site
http://www.rebeccawineintuscany.com/
On another trip, we did a day trip which included Siena and a couple of wineries. Could easily have done 1 or 2 more wineries if we did not spend so much time in Siena. we had a private driver and car.
I've also recently used this company which you could contact about driving you around on a winery tour just for the 2 of you out of Florence. We used them for a day trip to Montalcino from Florence. We did one specific winery with whom we had a connection as well as lunch and some time in Montalcino itself. We could definitely have gone to a couple of others if we only wanted to taste.
http://www.hillsandroads.com/inflash/index.html
Also if you are interested, you can go Antinori's newish winery which is just south of Florence. It is possible to take a public bus there from Florence. We walked to Porta Romana and caught a cab from there to avoid the maze of the limited traffic zone that a cab would have to take from central Florence. You have to book. We had a nice, if pricey lunch there after our tour. (took the cheap tasting and splurged on 2 excellent wines with lunch).
You haven't asked, but I will recommend a restaurant in Florence to you - https://www.tripadvisor.ca/Restaurant_Review-g187895-d1580679-Reviews-Trattoria_Osteria_Da_Que_Ganzi-Florence_Tuscany.html
Typical Tuscan food. The owner picks all the wine himself and loves to discuss wine with you if you are at all interested. Tell him you love wine and he will spend time discussing what he has. We had a terrific wine from his home neighbourhood which is a small production. Of course he has separate lists for wine, grappa and vin santo.
Also there are two very good wine shops in Florence - this one is outside the central area, but you could walk there
http://www.enotecabonatti.it/
They have a very interesting selection of wines from around Italy and make good recommendations. Sometimes they have tastings in the evening.
In the Oltrarno there is this shop
http://www.florencewinemerchants.com/buying-wine/enoteca-millesimi.html
If you like wine from Siro Pacenti or Valdicava for example, I think this is one of the few places where you can find them in Florence.
I have lots of other suggestions for good wine tasting in Florence itself. You can private message me if you want more information.
