Out of curiosity, where were you sitting that you could order wine, prosecco or champagne at the table? As in, what stall were you near/across? Just wondering if the wine is coming from the center (beer) bar, or one of the other stalls. If you sit closer to the corner with the seafood stall, the restaurant stall next to it will run wine to you if you ask - presumably if you're dining with them, but if it's slower, even if you're not. Didn't know about the other options.

You're already well into your day there, but I'm kind of hoping you order a Fiorentina from the butcher stall and tell us how it is :D I really wanted to, but ran out of time.

I was sitting 2 places - across from the burger place (on high chairs) and at a normal table across from the meat place to the immediate left of the burger place (la carne e i salumi).
The drinks menu has water/soft drinks on one side and beer/wine/prosecco on the other.
It was the usual drinks-people taking my order.
I have decided not to have the Fiorantine steak - looks like there is too much bone and irregular meat on it for me.
But I have had the Tagliata di Bovine from the meat place next to the burger place and that was a surprisingly big steak.
Their roasted potatoes are very good too.

Going in there now and have to decide what'll be my last meal there.......

Florence Restaurants?
 

I ate at Osteria dei Pazzi in Florence on the recommendation of an Instagram comment. They were reserved but when I mentioned the name of my Instagram friend (I've never met) the owner smiled and found me a table (apparently they grew up together in Italy) the food was really good and there were many families and groups. It's a funny story of how Instagram got me a table that I wrote about http://philatravelgirl.com/florence_solo_dining_osteria_dei_pazzi/
Social media and FT are great for highlighting hidden gems IMO