Fix drywall around a electric panel
Frame it with wood.  Make it removable.

The Victorians had a brilliant sensibility.  When they built bathrooms, they would build a small, attractive cabinet door in the wall on the other side of the tub spigot.  You need access to the plumbing guts?  Open the door.  It has proven indispensable.  

What looks like ugliness is in fact a godsend.  You have access to the exterior of the panel for adding more circuits.  That said, you still want fire protection. 

Since this is a utility space anyway, I would build a simple, attractive wood frame of 1x4's around the panel, bridging over those holes.  I would make the top and bottom easily removable.  Also set it back just enough the service panel cover is easily removed without removing the top and bottom.  

For fire protection, I would cut drywall pieces to fill those ugly holes top and bottom, and attach them to the back of the 1x4 framing.  That way the framing holds the drywall in place.   Want to add a circuit? Remove two screws and the 1x4 comes off, voila. 

Since it is a utility space that gets dirty fingerprints, I would attractively stain the wood. 

Thanks for the idea. I don't often embed service panels in drywall, but now I'll find a way to fit access points above and below, Victorian style.