Thanks to your efforts I now have a better understanding of the system, Bob. Wonder if it was that the drill wasn't set on 0 deg or if the stock wasn't shimmed up under the nose to keep its longitudinal centerline parallel to the bed? I shouldn't ignore the possible contributing role of a rounded off catch. Looking at Kuhnhausen, I see the 90 deg (-) callout on side of the catch to the short leg of the spring. If it's rounded off, it is also a tad shorter and, thus, has less bearing on the edge of the slot in the band (for a Type 2 or 3; from the outside of the band for a type 1).
I have an original Saginaw that the band occasionally pops off like yours. I didn't want to alter it or swap springs, obviously. The hole was tight, so I installed the spindle without pushing it all the way down. I rarely shoot it, but that seemed to cure it. Now I'm going to have to take another look at it to try to puzzle out which element (or combination) caused the problem. You didn't know it, but you were helping diagnose mine along with yours!
Can't do much about wood shrinkage or oversanding without using a shim, but absent those factors, I think this exercise may have produced a new diagnostic procedure: 1) check hole to assure it's not wallowed out - spindle should fit tight; 2) check location of hole on right side relative to stock stepdown (dimensions above); 3) assure catch is sharp on face and about .053" high; 4) and one more - where flat leg breaks, assure angle is about 12 deg and the angle of flat leg to spindle is about 83 deg (that's what makes it spring).
I just dug out a new spring that I got in a parts grouping. Had always suspected it was non-USGI. All measurements are fine except the angles - 87 deg + (should be 83) and 7 deg (should be 12). That's awful. It's in the trash. Glad there were some really nice small parts in that group otherwise.