I'm happy to announce the mouse update is now on the public beta branch!
All menus should work now with the mouse, clicking once to select an option and again to continue. Under control options, you can now turn on "Mouse steering", which will cause the ship to automatically turn to face the mouse cursor. I'm very happy with how this turned out and may consider it my preferred way to play now. The mouse buttons are now also bound to abilities, while the scroll wheel can be used to accelerate or decelerate. The player can use any combination of mouse and keyboard (mouse buttons all still work when mouse steering is off).
Still needs a little more polishing, and there are currently no in game explanations of the new options, but that will be coming next before it makes it into the default branch.