If you have any left over stone you might want to experiment with cutting narrow strips off - say 3/4 X 1/2" or thereabouts - and consider having them mortared around the perimeter to hide the gap. You can rent a wet tile saw yourself or have your contractor do this. I don't know if metal trim would work due to the irregular surface of the stone adjoining the surround. It would still leave a narrow gap regardless that would need mortar. I think the biggest issue here is the white sealant still visible. Get a putty colored grout mix instead for these areas.

So is the option of having a metal fabricator creating a simple frame from out of lite gauge steel. There are many narrow profiles available - and it's very simple, they just cut the pieces to length and tack weld the corners. Something with a bit of depth or a flange will do the trick. Then this frame will be mortared in place (not welded) snug up against the unit. It just needs a bit of Matt black heat resistant paint first.

PS: after looking again I have to ask you to inquire about that white sealant. Why is (what appears to be caulk) being used near a combustible unit to begin with!? Please ask whoever did this installation to verify, and do call your local city fire inspector as well.

Wow, thank you! First, the white is grout, so we are safe. Second issue - the fireplace insert is old and may, ultimately, need replaced or repaired. We are trying to bridge the gap while maintaining access - - i.e. something that could be removed separately or as part of the insert. Your second solution is our preferred one. When you say 'mortared into place,' do you mean onto to the insert, which would preserve the flexibility issue? If so, I'm curious, why mortar and not welding? Again, many thanks for your response, it is quite helpful!

If you are going to switch out the box for a proper insert I would do it. I've said a few times on the forum that conventional masonry fireplaces waste the majority of the heat they generate. Or better yet switch to gas. Read the following link to get yourself better informed, and do think about an insert.

http://www.houselogic.com/home-advice/fireplaces-chimneys/save-money-with-fireplace-insert/

http://www.epa.gov/burnwise/burn-wise-frequently-asked-questions