Class "A" doesn't mean it won't burn. Class "A" is a flame spread/smoke production rating. It comes from NFPA 101, Section 6-5. Class A, B and C correlate directly with Class I,II and III in most other building codes.
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The "safe" distance for any stove in the USA on the side(s) with the door(s) is 18 inches. It's typically less for the other sides, but it varies by stove. All the manufacturers have the instruction manuals on their websites with all the clearances.
So at 19" you are "safe". If you're still worried, you could put a metal lid on it, or skin the wood with metal for ember protection. Durock is non-combustable.