From the pictures, the casting quality of your aluminum Honorable Discharge emblem doesn't look to be very good, which isn't surprising if they were created via a simple sand-casting process (imagine how a photo-copy of a picture isn't as detailed as the original).
However, it must be related in some manner to the emblem shown on the cover of your Popular Science magazine from 1945. The design elements look to be identical, just lacking in detail on your aluminum version. In fact, I'd bet the emblem pictured on the magazine cover is fairly large, possibly the same size as your emblem. More than likely one of the originals was used to create a sand mold for the emblems like yours, which would explain the loss of detail.
I could certainly see them being used for grave markers, for decor at a building related to a military veteran organization (American Legion, VFW, etc.), or who know what else. It's more likely these are NOT official government produced versions, and likely made by a third-party who somehow acquired a copy of the original version emblem and used it to create these aluminum copies.
Does the aluminum show any signs of age/oxidation?
A molded copy makes sense. I bought the two of the three with the best detail. Both had oxidation in the form of a dark/dingy spotted coating, but not the sort you see from exposure to the elements. I cleaned the one pictured and left the other as is for later comparison.
Aluminum would have been available as a surpluss metal at the time, and makes sense if you want to save costs in shipping these copies. The rub for me on these is timing. The original design photos were sent to the press in mid to late September 1945. Prior to this a design existed for the Honorable Service lapel button, designed by Anthony de Francisci. With the removal of the "National Defense" wording at the top, Francisci's design became the Honorable Discharge lapel button. Those buttons began to be issued sometime in November and December 1945 as best I can tell.
My version of the eagle design was floated between September and November/December 1945, but then disappeared completely. It looks like it was meant to be a similar, but distinct design which was scrapped at the last minute. For it to exist in any form beyond the newspaper and magazine photos is what interests me.
Aluminum as the casting agent makes a lot of sense since it's an easy metal to work with, and I agree that this was replicated using a simple process, but who had ready access to aluminum in 1945 and a copy of the design to work from? Each of the three copies I have seen show a little less detail with each new casting, and a sand mold would explain why. I just wish I could track down where the new design came from, why it was changed and what samples may have gone out.
Thank you for your insight.