Sorry, one more note..
Thankfully we have not booked any of our train tickets
It's too early to do that as schedules/booking ability isn't fully loaded for that late in the year (they'll fully load on June 10th, I believe). Italo currently only shows through July. I was using random dates next month as schedules don't usually change much.
Again, I wouldn't pre-purchase tickets for arrival day (Rome>Florence) unless you can land discounted fares SO cheap that that you're willing to eat the cost should your flight be delayed, there's a long backup at immigration at Fiumicino, etc. and you miss your train. It will probably mean buying base-fare tickets but it's the safest way to go.
That said, Italo offers a Flex ticket that allows you to change your departure time/date up to 3 minutes before departure for no cost, and is usually available in multiple class tiers. They're priced higher but when figuring the fees incurred if needing to change a low-cost or economy ticket, could be a wash.
https://www.italotreno.it/en/support-contacts/faq?faqID={F8F504B7-2910-43BD-9150-7A7B5D5AF7D1}
Also, 2nd class/economy tiers are fine: there's not a big enough difference in comfort, IMHO, to warrant the price difference between those seats and 1st class/prima class should that difference be considerable.