I don't know why in the US people use carboys without any kind of material around them.
Since the mists of time in Italy the
dama, or
damigiana, which is basically the glass carboy, is inserted into a protection which is now typically made in plastic, but when I was a child it was in wood or rope. You can use glass if you like it, just buy the right stuff. That also protects wine from light and variations of temperature.
Foto circa Il vino dell'anno scorso Canestro di vimini. Immagine di retro, demijohn, anno - 45783212
it.dreamstime.com
Damigiana 25 L Birra Damigiane - Recipienti
www.polsinelli.it
Anyway in order to transport carboys or fermenter my back-saving strategy is to use a trolley, I use this one:
Carrelli master, diametro 350 mm, 150 kg, 821350: Amazon.it: Commercio, Industria e Scienza
www.amazon.it
Raising the carboy to the trolley is easy and fast. Then you move the trolley around your house, and then you put it back where you need it. You can make your own by assembling the parts, it's not a complicated object but it is useful.