I'd go remote. Professional installers often put the gear in a closet behind the FP wall. If you are able to remove the gear away from this area, paint the outlets so they match the wall color and fade away. I don't think there is enough room to justify cabinets, and you're right about the gap making it look odd. One thing I'd do would be to paint the brass trim on the glass doors. Matte black heat proof paint would do that job.

i don't know, i think a couple low cabinets with art above could make sense.
it would depend on the style of the cabinets, really.

You could do custom cabinets something like this:

Depending on your Budget You could Add the same stone or Concrete up behind the fireplace to create a Flat divider for your mill work to return against. If you go to my houzz page and search under Southpoint scroll down and you will see what I mean. The one in our job is a bit bigger scale but you could do something similar. I think running to the ceiling would help make the fireplace not seem so heavy . Regards Graham