Hey Mike, I hope you give that some consideration. Do not tell him what to do, imo, it will only inflame the situation.
Legally, you may be in the clear burning cord wood, as long as there are no additives, regardless of the smoke. But it sounds like a sensitive situation. The neighbor will want his butt kissed, not his work list increased. In the end that's what you will have to depend on, your legality. His sensitivity to what he can smell could be anything, he could smell a barbecue at 200 ft. There could be no eliminating that, only mitigating measures.
Talked to my senile neighbor today, he called after getting tossed off my friend/neighbor's property. I listened and he complained his foyer was not wired and I said "get it inspected and sheet rock it" (which he disputed). He was reaching out, which is rare, and I was able to get my six ft. ladder and belt sander back from long term loan.
Have to add, he called the fire marshall who told him to call the health district, which he did. Cannot say more on a public board, but you guys who build surely have an idea..