First, I would use NGS's online tools to quantify how much is the shift between HARN and 2011 in your area. We have the transformations from HARN to 2007 to 2011 using GEOCON v1 starting at 10.4 but you have to install the ArcGIS Coordinate System Data setup to get the files.
You still might need to convert from HARN or 2011 to WGS84. Which transformations have you tried? Any to WGS84? NAD_1983_To_WGS_1984_1 is a null transformation (parameters are zeroes). Try WGS_1984_ITRF00_To_NAD_1983_HARN (don't redefine to 2011) or WGS_1984_ITRF00_To_NAD_1983_2011.
Melita