Air gap between wall above insert

I tore out my old heatilator and tore the old stone face off the fireplace to drywall the room. When I did that the wall needed to be shimmed out a 1/2" so naturally without thinking i shot furring strips on and attached concrete board to that. On the top and sides the wood furring is on average 10" from the insert, however there is the air gap left over. I stopped laying stone about a foot from the ceiling when it hit me. I cut a strip from side to side that I can grout but i am wondering if the few strips of furring could get hot enough to cause an issue. The are ran vertical and there are only 3 above that are 4' and 2 on each side of the opening. Ultimately I guess my question is burying the furring in grout safe enough to not worry about it or get the sledge out and start over.

bholler said:

Show pics and what clearance does your inserts instructions call for. Burying them in mortar is not a fix at all check the required clearance it has to be in the instructions somewhere

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They opening I have is 37 wide 30 tall

After I removed the heatilator I put in a new mantle and re-bricked everything to ensure I had enough masonry

Ok here is what I'm having a hard time getting an answer from everyone even the manufacturer. What is the minimum clearance.
And if I can eliminate the combustibles to that point and grout the rest of the gap it would save me an imense amount of time and work. If someone could help me with finding these magic measurements I would really appreciate it. I would be more than happy to provide any more information about this unit or if there is an alternative unit that would work better that would be great as well.
Thanks

Is this something a licensed chimney sweep would be able to inspect and help me with?