Looking at the train schedule during the week (judging by current dates) the earliest train leaves at 7:30am arrives at 9:30am. We want to get there much earlier, we travel in May. Are more trains offered earlier then based on last years schedule? 5-6 am is ideal.

We may have to overnight there. we won't have much of an itinerary we are just going to do our favorite run (Arno, Piazza Michangelo down to Bobboli and back to Arno), lunch and maybe parts of the Uffizi We missed.

There is a train that leaves Mestre at 3:11am and arrives in Florence at 6:18am. It's an EN train and costs €22.50 one-way (about 1/3 the price of a Eurostar train).

You'll need to take a taxi from Santa Lucia train station to get to the Mestre train station for your departure. Not sure how easy that is a 2:30 am.

I think I'd lean towards spending one night rather than the slower 3am train.

New schedules will be entered on Trenitalia in a couple of weeks (usually around Dec 13-15). These schedules will be until mid-June, but I doubt there will be much change.

You'll need to take a taxi from Santa Lucia train station to get to the Mestre train station for your departure. Not sure how easy that is a 2:30 am.
Not that easy but you could have your hotel or place where you plan to spend the night arrange one in advance for you - just a thought.