Your "utility access" port is framed, I'm assuming around the perimeter of the hole...
I was thinking something similar to this, but instead of pulling a whole section out and having to use a grout line, build up a section to fill the hole, match your tile pattern, and then build up your blocking in the existing framework. You could either do a hinge and magnetic closure (kind of like a vanity door) or just use a magnet on 4 corners to attach the cover to the hole. leave a small "divot" on one edhe (the non-hinge edge if you go that way) for a finger grab pooint, or if you use the spring loaded mag catch idea, you don't need this, as when you push it in it will automatically jut out when you release it...
The main thing is to use caution, cut everything as close as you can, so the joint will be relatively unnoticable.