I wouldn't think the air mix adjustment would have any effect on the pilot flame. If there isn't enough air to support the tiny pilot flame, the burner isn't even going to ignite when the time comes!
Searching the internet, I found a first hand report from someone with a similar problem who finally figured it out after several attempts to fix the problem. I've summarized the final solution here:
"The water heater started and ran perfectly, with a good blue flame, but the pilot light was yellow, large, and lazy. After a day there was enough soot build-up to fill a teaspoon... I dismantled the main burner and pilot assembly for inspection [and] noticed that the pilot light tube was constructed as a Bunsen Burner, with a small fixed size air hole in the side of the pilot tube. This hole was normally concealed from view. If this hole was partially blocked, then the symptoms would be as described. I could see no blockage, but the tube is narrow, and the partial flap at the flame end makes it difficult to inspect. I dismantled the pilot tube using a wrench [and] I used a wooden toothpick to slide down the tube to clean it, and then blew down it from both ends.
I reassembled the pilot and burner tube. The water heater pilot is now blue, the automatic re-lighter is content, and so am I. I suspect this problem has been gradually building up for a few years. "
