How and where to day trip from Florence

Wow, that is a lot of time spent on trains for 2 weeks! Whether you want to take away time from Florence to add yet another destination to an already very full itinerary is up to you. Figure out what all you plan to see in Florence and estimate how much time you need to see it all before you decide on that. I would not break up your Florence to Positano day at a hill town unless you were going that route by car. One idea would be to stop in Lucca on route to Florence from CT since that is not as long a travel day. You also did not mention which hill town interests you, which would determine whether you take a bus or train. Or even better, join a one day tour of the Tuscan countryside! There are several tour companies based in Florence which do this and they have a variety of different itineraries, some stopping in several quaint hill towns for a couple hours each and some stopping in wineries.

You could take the bus from Salerno to Positano instead of a boat.

I have been taking the CV for thirty years, but lately it is horrifying. Crowded like anchovies and perfect conditions for thieves. Avoid it if you can, be extremely vigilant if you can't. If you have to backtrack to the Napoli Centrale station, as it seems you do, consider checking your luggage at the Napoli station and only take a small bag to Positano for your two nights there. You will be less of a mark for thieves.

I see that there are fast direct trains from Florence to Salerno in September, that take about 3.5 hours. Then you could take a bus or maybe a boat to Positano. That would probably be a more leisurely day than dealing with the CV train from end to end. And to your other question, certainly you could easily take a day trip from Florence to Siena or another hill town if you wanted. A day long tour including a couple of hill towns and one or more wineries, maybe with a luncheon at a winery, would be very enjoyable although more pricey. Although you already have five days of major travel on your itinerary, in addition to your flights.

After watching Rick's TV episodes in Tuscany I was leaning toward Orvieto or Montepulciano, but it seems these might be more difficult without a car. We would like to go to a vineyard or maybe an olive grove, something involving the Tuscan cuisine, but I guess that can be done in many of the hill towns. I think we would rather go to one, maybe two, hill towns than ride around to several different ones in one day, but if we could find a tour that would solve the transportation issue that would be great. Are there any recommendations for such tours? I've looked at Walks of Italy and those seem a little pricey for us.

Lucca does seem like a convenient option- it just has not stood out to me in reading or watching Rick's show- is there something I'm missing about it?

How much might it cost to rent a car for one day from Florence to drive ourselves southward and then return to Florence?

I do think it would be easier to take the direct train from Florence to Salerno (3.5 hours), then take a bus from in front of Salerno station (where it starts out empty) to Positano. Boats also run in summer.

On your third day in Florence, my first choice of a day trip would be by bus to Siena (1.25 hours each way by "Rapida" depatures). Italian bus services run much less on Sundays.

I cannot imagine adding any more to this schedule. I would say, try to relax a little and enjoy florence. Or you might consider a lovely meal in Fiesole overlooking Florence.
Someplace like this:

http://www.lareggiadeglietruschi.com/