In 9.3, we didn't have a NAD 1983 UTM zone 13N that uses US survey feet. We have added one in 10.1 (WKID = 4433) but you would need to create a custom definition. You could create a .prj file that contains the new definition and create the coordinate system from that. You could also convert your input data from feet to meters and use the standard UTM zone.
Is there a transcription error in the conversion value?? It should be 3.28083333333333. In meters, you have values at 5 and 6 places even before crossing into decimals, so you need to use a conversion value that matches the desired precision, and probably has at least 1 or 2 extra digits.
IProjectedCoordinateSystem2 has PutLinearAndAngularUnits method. That might work.