Without a $200 tax stamp and a 9-12 month wait to get it, you're stuck with an 18" barrel as the minimum for a shotgun.
However, for a short overall weapon, I suggest a bullpup shotgun like the Kel Tec KSG or KS7. The KSG holds 14 2 3/4" shells in twin magazine tubes, and the KS7 holds 7 rounds in a single magazine tube. Both have 18 1/2" barrels, but their overall length is only 26".
Kel Tec KS7:
