The 1" from the edge actually sounds pretty normal to me. You are seeing the pattern from a full pass. While a lb. or two drop may be needed, i don't think you were way off. A look at the track footprint on launch may show that you are indeed getting full contact at that point.
The "one" tire pattern could be suspension related? Or even out on a limb, a sure grip not quite locking up? Or do you have a spool?
What width wheel are they mounted on? Might help others chime in with similar setups.
P.S. I know I'm getting long winded here :D, but how many passes are on those tires? Even though most slicks have directional arrows, whenever mine would get "grainy", I'd flip them for 2/3 passes and that would clean them right up as long as they were still within their service life.