Is there a place in or near the Florence train station to store our duffel bags for the day while we explore so we don't have to lug them around?
Yes, there is a Deposito Bagagli at Firenze S.M. Novella station. Note that Florence has more than one station, so you'll need to specify the correct one when buying tickets. Here's the information....
I'd suggest allowing lots of time both to drop the bags off as well as pick them up. There can be long queues.
We used the "Left Luggage" service twice a few days ago. Worked slick. Hard to see where it is at Florence's SMN station...next to track 16. Look for the McDonald's and keep walking a bit further down, so you're walking parallel with the train tracks on your left. It's hard to see because some restaurant signage blocks the bag sign.
We were lucky to not have to wait in any long lines...but a group of 20 kids came right after us!