I just wanted to plug Icomoon ( https://icomoon.io/ ) -- They will let you assemble your own custom font icon set using subsets of public glyphs such as FA, and your own SVG images. I Hope this helps someone.
I use icomoon and it is definitely helpful but I must say the UX for creating icon sets is quite scary to use. Clicking on an icon by default removes or adds it to the icon set, so its incredibly easy to exclude an icon you are using already (meaning next time you publish your font, that icon will no longer render on your page)
Yeah, I've done this countless times, only realising once I have packaged it into my project. I ended up creating a Webpack loader which takes a small JSON file and creates an icon set for my project. I could consider releasing it on Github if there is interest in something like this?