I don't know if it is a possiblity with your Vespa - or even if you would want to consider it, but years (and years) ago, we owned a UK designed 20' travel trailer called a Sprite and we carried a Honda C70 scooter inside it!
The Honda scooter is the step through design and carries two people - has much larger wheels than the Vespa. but is probably narrower than the Vespa.
I just made a wooden ramp to run it up onto the trailer and we carried it in the aisle between dinette and galley.
I remember having huge pieces of foam on either side of it.
It worked fine and we took it an many trips - never caused any damage to bike or trailer furniture. To the best of my knowledge, I don't think I tied it down in any way, it just stayed on its side stand - which seems a bit foolish now I think on it, but as mentioned we never had the slightest problem and it was a lot of fun having it along with us.
The bike we have now is a bit bigger so I don't have this option!
Brian & Connie Mitchell
2005 Classic 30'
Hensley Arrow / Centramatics
2008 GMC Sierra SLT 2500HD,4x4,Crew Cab, Diesel, Leer cap.