Have you tried construction adhesive?
This product works well: https://amzn.to/2HosJLB
Hope this Helps! Jeremy - https://do-daddy.com
Avoid putting the wood within 18” of the firebox, as that’s Building Code.
My neighbor from the old school in Italy, put tile over his ugly brick fireplace, very easy and variety of choices. Of course those old times know how to do all that. I have since moved and am going to do it with this ugly orange brick, can't match paint to the color, after 3 attempts at wall color, time to cover the brick. Best of luck to you.
Maybe try a whitewash before covering the brick. You would be amazed at the difference, there are may postings here on Hometalk, I also posted my journey "massive brick fireplace wall whitewash success"