The OP's statement above in bold is the reason for the taste issues. I don't load the meat for at least an hour after loading the hot coals. It takes that long for the smoke to show hits of blue and a clean burning fire.
I'm biting my tongue about the charcoal used because it is so popular. It works in a smoker, but loading meat too soon will only magnify the taste issue.
Yeah, from the replies here it seems like that is the change that will yield the biggest improvement. And please, do chime in on what type of charcoal you prefer. I use KBB due to so many reports of the WSM being pretty much designed for that exact charcoal structure and size (even more so than Weber's own charcoal brand). I've seen reports of problems in the WSM when more exotic charcoals are used, but if you have other experience please share!