heat shield construction

I am in the process of building a new heat shield for my Chubby. My wife and I have decided to install Elderado Stone over cement board behind the stove. I'm torn weather to use construction PL or lath and morter to adhere the stone to the cement board. I've researched both products. Elderado Stone installation recommends using lath and morter. We have a construction crew on my job that is installing Elderado Stone using the lath and morter method with poor results. The stone doesn't seem to be holding that well. They started to use construction PL with greater results. However, Loctite construction PL suggests using in temperatures below 100 degrees. Not sure if this product is safe to use within 12" on my stove. Hopefully someone has some experience in this area. Any information would be greatly appreciated!

Are you attaching this to anything like a wood stud wall?

Being a stone mason,I would go with mortar adhered veneer instead of glue. The glue may become soft and not stick with the heat, I never had any problems with stones not sticking. I would also find another mason if they can't meet your expections.