I did make some progress on getting the 81E back together. Bore is very straight and true; could be an "A" with just a touch of wear or a "B" with very little wear. I can't find any markings on the cylinder so I am leaning towards the "B" as that was the default. Piston is a bit scuffed but I didn't want to put a new piston in this one without being positive on the right one so I cleaned everything up as best I could and used it anyway. I checked it before tearing it down and it was making 150 PSI so I figure it will still run all right.
I did set the standard late model electronic ignition coil on this one and it certainly fits properly. I will put it together with the real ignition set up and try to check the timing between the two using an electronic timing light while spinning the saw over with a drill.
Here's how things look so far.
Mark