Reload all fonts without restarting an app
Someone may have a better solution, but here's an explanation and potential workaround.

The problem you're having is that you're editing a font already loaded by your applications. In other words, while macOS has been able to dynamically add fonts to application menus since the onset of Font Book (although it often didn't work well until Mac OS X Leopard was released in 2007), it's not able to trigger the fact that the font itself has changed.

My best guess at a workaround is to just use Font Book to Disable the font and then to Enable it again. This should force all your open applications to register the change because the font has been enabled again.

As an aside, you may find this page of interest to you: Font Management in macOS and OS X.