Bad hoops can cause the same symptom, but yours does appear to be the shell. I would take all of the lugs off and measure from each lug to see if they all wander or if just one or two are off using a flexible measuring tape. Measure from the left side of the hole on one to the left side of the hole on the next. Since you are using the same reference point on both, it is the same as measuring the center to center measurement and is very accurate. If it is just two that are off, the solution will probably be to file the holes in the direction they need to go to be the same measurement from lug to lug. Assuming they are off by only an 1/8" or so this should be doable with no evidence from the outside. The lug mounting washers may cover this up on the inside as well.
When I first noticed this, I did take the lugs off and measure with a soft tape measure. The punched holes are off for sure. They do not looks egged out or anything. Perfect nice holes, just spaced wrong.
The rims are a little egged from having been pulled by the lugs but that not what is causing the trouble. I thought about filing the holes but then did not.
I will take a Horizontal :) picture of the badge. It looks normal to me, similar vintage and serial number to my Slingerland kit (obtained elsewhere).
It would make sense if this was somehow a later shell when things were going downhill-but the serial number is earlier-unless the badge and shell are not from the same time.
Erich