You should define your idea of 'short barrel'.
Benelli makes their auto in an "Entry Gun" format with a 14" bbl., though it only has a five round tube. The gun averages about $900, + the $200 NFA transfer fee. With the smaller shot sizes that most folks load for inside the home defense, it would be manageable in recoil.
Of course, if an 18" standard bbl. is acceptable, you could get a Mossy 9200A1, but it has a standard 4rd. tube. the full size Benellis are at either 19" or 21", IIRC. Ditto for the Remington series, I think. Most folks feel that the gas operated guns have a bit less oomph than the inertial action of the Benelli, given the same load.