So I burned some United frequent flyer miles instead and am going to fly from Frankfurt to Vilnius, wander around in Lithuania, Latvia, maybe Estonia, and possibly northeastern Poland, then fly from Vilnius to Florence and look at bits of Tuscany with KJ.
This works much better, I think. If I had a month or two I'd take the train. The train's more fun. If I were staying for a month the disruption to my schedule on blowing a connection wouldn't be such a big deal.
As it was the rail journey was starting to look like something Phileas Fogg would do. In other words, fun. :)
Ah well. Next time.