Interesting cover. Yes, I definitely agree with the recommendation to send it in for a certificate before the return window expires. How thick are the "stamps"? Are they normal stamp thickness, or are they printed on a thicker paper or cardstock?

It is hard to tell from the scan, but from the darker shadow at the right edge, it looks like it could be a thicker cardstock, meaning this may be a plate proof illegally used as postage. Also the gap in the blue crayon marking where the stamp meets the envelope, especially on the "4" makes it look like it is thicker than regular stamp.
As No1philatelist said, "These items were not regularly issued, but rather were sold or given to favored persons." An official from the Finance Department could definitely meet that criteria where he received some samples as proofs, and later accidentally or intentionally used them to mail a letter.