Reddit mentions of Thomas & Betts B1EXT-CRD PVC Elec BX Extender

Nice clean little setup you have there. Good job. My inner electrian is getting bothered by your receptical though. They make box extensions so that your receptical can be flush with the faceplate and look finished also safer. Not that you will probably ever accidentally stick a screwdriver or something metallic in that way but... again.... My inner electrian had to say something.

Like this, there are a lot of different options though.
https://www.amazon.com/gp/aw/d/B000H5ZVY8/ref=psdcmw_6369374011_t2_B00J7I2446

Edit: just realized that that receptical is cracked too! Put A GFI and an extension on and you'll be good to go ;)

Doesn't need to replace the box. They make box extensions like this and this and handy box extensions.

He might be able to remove the existing box and install an old work box behind, and facing the other direction, from where the original box is. Other side of the wall. Although, abandoning the original box location may be a code violation by removing a required outlet location.

2nd vote, for chipping up the entire tile floor then. If its ALL damaged and worn, just rip it up and replace it. If the holes in the existing concrete are near the tiled area, just run the tile into the next room and cover it all at once. If the holes are under where tiles are broken now, then just fill it in with mortar as you redo your tiles. Small gaps won't be a problem.

I totally should have thought about running new drywall over the existing wall. That's a MUCH easier option. And if I recall correctly, they make little electrical box extenders for this type of situation.

http://www.amazon.com/Carlon-Pvc-Electrical-Extender-b1ext-crd/dp/B000H5ZVY8