Convert light fixture to receptacle
It looks like you have a standard box and not a light box. So you don't need the light box receptacle cover. In theory, you should be able to add the receptacle without issue and just use a standard outlet cover.

You can split the hot side by breaking out the tab. Assuming the nutted blacks run to the switch, you can add another hot and wire it to the top "always-on" outlet, and let the switch power the bottom.

The only downside I see to this is they're grounding to the box. Without knowing if the box is grounded, you might not be getting any ground at all if they just screwed it to a wood joist. If the box is grounded, what you'll need is a grounding clip and then run a wire from the clip to the outlet.