I happen to have my own notion of that possibilty (merely a different area of the same airplane) as many have seen I'm sure.
I'm certainly open to other suggestions. The tricky thing is finding a span of .032 skin that long (24 inches) with no crossing line of rivets.
Anything is possible - including any number of source locations on the Electra, of course. But what you've pointed out, actually seeing the artifact in person and the Harney drawings are all what got me looking at the lavatory window covering that was installed as a field effort in Miami.
That window was very large - at least 24 inches in fact fore-aft (from just aft of Station 293 5/8 to roughly Station 320 - a bit over). As evidenced in the pictures of the window in its open condition, there was no intermediate bracing - the outer frame was substantial. To cover that would not require crossing rows / intermediate bracing (across the rows we see). But some form of bracing to offset oil-canning / timpanic effect would be advisable, hence the rows of small rivets, IMO, as a possibility.
Prior to seeing Harney's drawings at the symposium in June 2012 I had not realized that this window had been cut into the Electra, then covered over later as decided unnecessary by Earhart and Noonan, apparently. It would not take much in the way of 'structure' to effect such a cover - just light guage metal, as we see (which also happens to be consistent with skins aft of Station 293 5/8 I'm told). The use of 3/32" rivets for light stiffening would be ideal, especially if the owner was fretting over weight concerns; there would be no primary structural challenge - the outer frame for the previously installed window would continue to bear those loads quite effectively.
See pictures here of the window prior to covering, then covered as done prior to departing Miami. Finally, I've illustrated the conjectured use of light stiffeners spanning the panel fore-to-aft, which would reasonably fit what we see - light (3/32") rivets in slightly irregular rows, as if hand-drilled in field as after-thought or perhaps just an improvised / expedited effort to stiffen the rather large tempanic covering.
This is all just an idea of course, but it made a lot of sense to me as a possible source for such a large, light-guage panel with evidence of light stiffening having been attached in the past (my read of the rows of 3/32" rivets).
One other aspect of the cover being in this area is that it might be particularly vulnerable to any explosive force (water?) that was trying to escape the cabin / lav / tail area of the bird. The large surface area covering a fairly large compartment with little baffle effect to stifle the force could leave the cover easy prey to overt force like that; it could be largely knocked out, and any remaining fasteners / seams then subject to rapid fatigue as the panel might shift to and fro with nature's forces (or someone salvaging an opportune piece of metal). That may fit what you've described as forceful removal of this item from the craft. A belly skin might be problematic in that way, considering that the flooring might serve as a baffle against the offending forces, just a thought.
Is there more information on the window covering effort that was done in Miami? That might be an additional area of study to see what can be learned. It is entirely possible that the photos are the only evidence we have - as a minor alteration done in haste, it is possible that no record was made of this effort. But, with the artifact in-hand, that area of an existing Electra might be studied for similarity to rivet patterns along the edges - realzing Earhart's was altered with a substantial window frame, of course. But maybe there is some additional information somewhere on that mod as well.
In my mind, the lav window covering could be a real link to this mysterious large, thin piece of metal - that sort of thing would not turn up too many places, certainly not as a sister member in primary structure IMO.