A cleaner burn will certainly help, however, something new to add to the discussion is that the previous life of the wsm may play into this.
This is from page 10 of the Harry Soo pdf:
<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content"> Seasoning your smoker: It takes a while for a WSM or any pit to develop the right aroma and bark/gunk on the sides and dome. I wouldn't recommend you enter a contest with a new pit. I season my new pits by cooking bacon strips or scrap pieces of meat (e.g. pork trimmings) to generate oil vapors, smoke, and grease to coat the inside. I think it takes at least 10 cooks for a WSM to develop the right "seasoning" for consistent flavor. Whatever you do, never cook hot dogs or fish in the same WSM that you use for cooking ribs, chicken, pork or brisket. Get a separate Weber kettle for hot dogs, hamburgers, fish, lamb, etc. If you've ever tried smoking meat in a pit that was previously used to cook hotdogs, you'll know what I mean. I find cooking ribs and chicken in a pit previously used to cook hamburgers affects the rib and chicken flavor. Remember my frame of mind is winning contests. Aunt Martha probably wouldn't notice much. A CBJ on the other hand, would! </div></BLOCKQUOTE>
I'm not sure how much of this I buy into, but I do know that my bbq has a certain flavor, that no matter what I do, I can't shake. I'm considering giving one of my wsm's a serious cleaning and starting over with a new brand of charcoal.
I'm thinking that its possible that your meat is picking up flavors from the wsm as it heats up.
just another hypothesis for you to consider