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Fat tyres with for the fun!
I'd go with the Krampus, yes there will be sections where you will want a sleeker roadie ride, like the Izoard or Agnello, but that would make all the strada far less fun (especially in the uncertainly wet conditions of May - snow melting and all that)
Plus you'll have a bikepacking setup anyway, just accept that this is about having the most fun, not smashing any time on Strava.
That should also sort your carbon frame vs plane doubt.
I've just booked flights to ride this route in May. I have two bikes that would work but can't decide , Genesis Datum with 38 mm cross tyres and ultegra or Surly Krampus with Carbon fork ,2inch small block and 1x11 ? The Krampus is heavier but it will be more comfortable whereas the genesis is lighter and faster but I'm a bit concerned about putting a carbon frame in the hold of a plane . Cheers