I'm a bit short on time, but I'll try to get back after my shock treatment...
My WWL had similar issues. Too numerous to quickly mention, but for the most part, I'm happy with my unit now.
Let me hit a few issues you might have addressed already, and list a few suggestions:
Draft may be an issue, but that may be hard to determine. I tried taming my draft once with an 8" to 6" reducer to combat over-firing. I discovered that the reduced draft immediately resulted in smoke exiting the door when burning it open. Especially when starting a fire, which was made difficult without smoke entering the room. Removing the reducer put things back to normal, allowing cleaner kindling, but still difficult to control higher burn rates. But I knew I didn't have excessive draft. At least initially. If you can build a fire and burn with the door open for the first thirty minutes, it probably means you have a decent draft and will experience less sooting. If I close the door too early, the left side really soots up quick, and bad.
After 1/2 hour open door burn, I close door and let 'er rip for another 1/2 hour (at least) before thinking about engaging the cat. I also am careful how I load the stove. I leave 1 inch of ash to cover all ash grate 'air holes'. I stack all wood touching one side or the other, usually staggering pieces so some touch left, some right. This helps get flames side to side and reduce sooting on the glass.
The glass is HUGE! I'd guess that most glasses this large have a hard time staying clean. Add bad primary air flow, one sided intake, holes in the stove bottom allowing air up that left side gap between fire grate and left firebox casting where little air wash is present, smoking wood close to that area, and you have a creosote mess on the left side, bottom glass.
Just changing my burning habits helped tremendously with the sooting. I can actually burn it off sometimes, which should be impressive to any WWL owner.
When I add wood (I'm getting off on a tangent, but these things have worked for me), I rake coals to the front, near the glass, and add wood no closer than two or three inches from the front grate. Hey, it works for me.
Of course, the WWL has lots of 'issues'. My first firebox (stove without the surrounds) looked like it was assembled by children. I am on my second box now. It at least has a flat gasket sealing surface, or should I say surfaceS, since the design depends upon luck in assembly to make a good door seal.
Have you plugged all the holes in the ash pan compartment floor? There are probably two missing leveler feet and two mysterious holes about 6 inches apart just an inch from the front. Plug them all. I used bolts for the levelers, and nuts and bolts for the mystery holes. Air comes up from below and makes its way either up through the grate, or if you leave ashes like I do to protect the grate and prevent some heat loss down below, then the air goes up through the two sides of the grate in the front that I still haven't plugged up. Keep meaning to do that. I can see condensed creosote on each side of the ash pan door where I suspect air is still leaking in there from either the almost plugged mystery bolts, the lower door gasket or somewhere I've missed.
Do a 'half-dollar bill test' just above the lower hinge. This is a potential trouble spot where the firebox castings 'meet'. Use a dollar cut (or folded, but it's double thick) lengthwise so as to not span the upper and lower castings.
I have a similar sooting pattern on the left as you do. I agree with Steve about the intake air side, coupled with your analysis of the manifold air flow pattern = left side sooting, potentially big time. I combat this fairly effectively after learning to burn with discipline.
Sad, but required. I burn the first half hour of a new fire with the door open and a fireplace screen in place. This gets the fire going good before I close the door for the second half hour. I'll often go another 15 mins to 30 mins until the cat probe thermometer shows >=500*F. I can usually light it off after the first hour, but the extra half hour can sometimes make a difference in sooting if the wood splits are really big and not yet 'rolling'.
It took me the whole first season to start getting familiar with this thing (3 cords) and another two cords to get to where I can pretty much keep the glass clean. Oh, I almost forgot, I operate based almost exclusively on cat temps. I feed no more than two large splits, three or four smaller ones (half full firebox load), when the cat temp is between 800 - 1000*F, and I let them get going good before I think about reengaging the cat, maybe 5 - 15 minutes, depending on the wood's temperament. It needs to be charred and/or burning on all sides before reengaging the cat. That is the secret. Keep everything hot. I don't put in TOO much wood, or things get a bit too hot, but essentially I burn smaller, hotter fires, and manage the wood and coal location in the firebox. It takes a bit more tending, but keeps the glass fairly clean.
Got to go, doctor is here... I'll check back after I wake up...