You have another option....
Italo trains also service Florence> Rome and Venice> Florence at competitive rates.
https://www.italotreno.it/en
As with Trenitalia, the cheapest tickets in advance will also have restrictions on the ability to change them at all or without penalty. They do, however, have a flex ticket that allows changes at no cost up to 3 minutes before departure of the train originally purchased.
Click "Flex" on this page:
https://www.italotreno.it/en/the-train/fares
These tickets will not be as cheap as the very lowest-price ticket tiers but will be less expensive than for higher-class carriages plus allow you the ability to make a change if desired. Just a thought...
We've only traveled smart/economy/2nd class carriages as they're plenty comfortable enough although some folks have been able to get a big enough price break in advance on 1st class/business class to justify the price difference.