I don't seem to be able to attach files, so here is a link to a zip containing my original AI files, the SVGs I converted them to, the resulting TTF, and some relevant screenshots.
Here's the weird thing. I installed Linearicons. It works fine in those other programs. In Photoshop, I'm getting the same font substitution I got with my own custom font. Both Linearicons and my font, "sacredfools," are showing the same generic rounded font when I try to use them in Photoshop. If you look at the "5 Photoshop example.jpg" file from the zip I previously uploaded, you'll see the font I'm actually getting. These seem to be identical to a font called "Gulim" which I cannot uninstall because it is a "system font." Gulim is meant to be a Korean font, but I only see Arabic characters when I open the ttf - and they're identical to the font I'm seeing when I use Linearicons or my own font.
Also, Photoshop is not listing those my Icomoon fonts in the main alphabetical order, but has grouped them in one of several separate alphabetical listings at the end of the font list, along with Arial Unicode MS, Gulim and several other fonts.