I am glad to see you have made so much progress... Good Work!
The dieseling is always a result of the throttle plates being open too far into and exposing the enrichening holes. You closed up the throttle plates and virtually eliminated the dieseling... Again, Good Work!
I am a little puzzled by your great idle RPM 620-ish with the speed screw in only 1/8 turn. My experience has been you get 620-ish idle RPM at 1/2 turn in, and that is the place where you find some vacuum to ZERO vacuum at the "S" port.
This certainly appears to be the place where I would start DOUBLE checking things like, is the choke coming completely closed and not hanging up on the fast idle linkage of the choke.
Another thing to DOUBLE check is the rod/cable linkage allowing the throttle lever to come to a complete closed position.
I think something isn't allowing your throttle plate to come to a complete close and that is why you are getting a reading of 1/8 turn in on the speed screw.
This may seem like an obsesive compulsive tweeker trying to tune stuff, but the Weber is a sequentially timed device, where it starts on the idle circuit and ever so slight throttle opening gets enrichening holes, then starts tipping in the main circuit and then additional enrichening from the accelerator pump nozzel.
This is why I continue to acheive the consistant maximum of 1/2 turn in on the speed screw, finding some vacuum at the "S" port and then backing off enough to get ZERO vacuum. Then we can continue to tune or diagnose the objections in performance.