Hello Eli,
Perhaps you can try supply a projection file for that layer. In ArcPad, you can find a copy of NAD_1983_StatePlane_NorthCarolina_FIPS_3200_Feet here:
"C:\Program Files (x86)\ArcGIS\ArcPad10.2\Coordinate System\Projected Coordinate Systems\State Plane\NAD 1983\NAD 1983 StatePlane North Carolina FIPS 3200.prj"
Take a copy of this file and rename it in a name consistent with your MrSID file and/or JPEG file with the extension set to ".prj". i.e. "NCMECK006017.prj".
Then next time you add this MrSID file to ArcPad, ArcPad should notice the PRJ file and it will use that file rather than trying to "guess" it from reading the MrSID.
Stephen