This might work but I'm not 100% sure.
In the gs\gs-whatever\lib directory, copy the sample file FAPIcidfmap to cidfmap, then add some lines similar to the following at the end:
/MS-Mincho << /FileType /TrueType /Path (C:/PSFONTS/msmincho.ttc) /SubfontID 0 /CSI [(Japan1) 3] >> ;
/MS-PMincho << /FileType /TrueType /Path (C:/PSFONTS/msmincho.ttc) /SubfontID 1 /CSI [(Japan1) 3] >> ;
Obviously, change the file paths as appropriate. That should allow GS to map the font names 'MS-Mincho' and 'MS-PMincho' to the TTC file.
Then you might be able to add an alias for 'Shingo-medium' to 'MS-Mincho' in the file fontmap. I've never tried that, though.
A more brute-force approach in cidfmap might be possible as well:
/Shingo-medium << /FileType /TrueType /Path (C:/PSFONTS/msmincho.ttc) /SubfontID 0 /CSI [(Japan1) 3] >> ;
Again, I have tested none of this.