Open backs in an "A" scale are not uncommon. Bob Carlin had one at the Mariposa Folk Festival many years back. Since you can capo to play in A on a fretted banjo, this isn't really necessary, however it's a good idea for a fretless banjo since the capo doesn't work on them.

Some folks move the bridge of a fretless banjo closer to the middle of the head to tune up and shorten the scale, but there's only one place for a fretted banjo's bridge, no matter what the scale.