What type of banana? What size?
Simon.

They are a 3 foot "Double Mahoi" and a 6 foot dwarf Orionco"

A dwarf orinoco will survive the garage. About the double mahoi i am not so sure. A bathroom might be another place.
Anyone another idea?
Simon

How about buying a cheap doormat type rug to put under the banana? Not the most aesthetic thing but better than ruined floors!

I cannot comment about the types being well suited to cool storage but most people that go for cool storage also go for dry and dark. If these cultivars will withstand the temp then consensus has been little to no watering and as little light as possible. Definitely not light trying to keep them growing such as you suggest. The low temp, dryness and darkness will force them to dormancy. Practiaclly the same as storage under the house except they will be in pots. If they don't go dormant the temp will probably kill them or cause considerable loss of pstem. I can offer no more as I have not actually done dormant storage myself.

I dig my banana's and put them in pots in the garage-which is also attached to the house. No extra light and I don't water them. When I dig them up I leave the soil on just because when I started with banana's I didn't know any better and its worked for two years so that is what I am doing again this year with most of them. Haven't gotten all of them dug yet and garage is full so I am going to have to change my ways...