While perusing the DC Municipal Regulations on another matter, I ran across this:
2400.8 A person may park a motorcycle or motorized bicycle in a direction other than parallel with the edge of the roadway, including perpendicular with the curb, if the motorcycle or motorized bicycle does not obstruct the flow of traffic.
Well, hallelujah. When I wasn't paying attention, DC added this provision. A recently as a year ago, there was a hyperactive parking enforcer on Capitol Hill who wrote me up all the time for "failure to park parallel to curb." Sanity prevails, at last.