The HotRod is what is called a "keyboard encoder" it transforms button input to keyboard input.
Of course, mGalaxy is smoothly working with keyboard input. Set the key you want to map on mGalaxy_Runway, then map this key on your controller.
If it doesn't work the problem is coming from the HotRod. You can easily check it by opening a text file and see if the button you press on the HotRod returns the correct character in the text editor.