Terry -
I'm pretty durn sure the issue was not one of using the wrong medium box. The "other" is 8 ½ x 11 x 5 ½", way different.
The fact that jpfabricator had similar problems lends a bit of credence to my original supposition that their dimensional control isn't too great. The aluminum box would (with a bit of difficulty) slide part way into the flat rate box, then the box would rip at one of the long edges. This happened with two different boxes at the in-store PO. As mentioned, I ended up taping the ripped edge back up. If I'd been at home, I'd have opened the glued seam on the box, wrapped it around the aluminum one, and re-glued (and taped over) the seam. This would at least have concealed the fact that there was a (small) size issue.
Maybe acquiring the box though mail order would tap into the PO's stock of "good stuff." I do plan to try this next year (or whenever the next pass around happens). Thanks for the tip!