I've done UK to Athens a couple of times last year and one-stop is the way to go. Don't make more stops than you have to unless you are on vacation! Your TB20 should have more range than my Caravan so make that stop at Cannes - easy to use, cheap and quick.
Routes were :
CPT - N859 – DRAKE - A34 – KOVAK - H20 - DOMOD – A3 – NEV – R161 – AMFOU DCT LFMD
and
DCT SODRI – A3 – ELB – A1 – CDC – L869 - CRN
G8 – ARA – B34 – DDM – B1 - ATV - LGAV
Just reverse from your end. Once you are up there request direct routings to cut off any corners.
At FL090 and FL100 you don't need oxygen and routing up the west coast of Italy keeps you out of the busy Rome area, gives you a great view as well as dry land if you need it. Same with France - keep well clear of Paris and life is much simpler.
Long day but it is a day trip........enjoy!