Update: Thanks for all the replies and advice so far. I found seat61 super helpful, and I wrote to the author with a comment and question and he replied promptly and kindly.
We got trains for Edinburgh to London, London to Paris. Seemed like an easy decision.
For Paris to Florence we looked at flights, but prices were volatile and went up sharply around when we looked, except for flights from the remote BVA (certainly seemed like not a good idea). We nearly got the flight from Orly to Pisa on a budget airline, but the prices went up, and I found that Thello recently (in March) provided reduced fares for their overnight trains that were previously only available for their daytime trains, providing 40-60% off the standard fare for a compartment for 2. The website was a little glitchy, and I had to get a more than lowest fare for the Milan to Florence leg in order for it to all go through. In the end, the price was competitive with the airline when factoring in ground transport to airport and staying in a hotel in Paris or Italy. As well, we figure the overnight trains seem to be getting phased out as more high speed trains are deployed, and we wanted to experience a bit of the older overnight train while they last.
We found a bargain price on Czech Air from Pisa to Prague, though considered the train passing through Vienna with a short stop there.