The 38-55 is not an option. The regulations specify a list of cartridges that does not include the 38-55. There is a catch all category:
"Center-fired straight-walled rimmed cartridges chambered for handgun use with bullets from 0.357” to 0.500” diameter with a case length from 1.285” to 1.800."
It doesn't appear the 38-55 will fit this criteria. No logic to this as the 375 Winchester is allowed but it is what it is.