If ownership is controlled just by the name of the Mii's Creator, editing that would be absurdly easy.
However, if not, we may have to find some other way around it, but who knows what effects it could cause.
I don't have the resources to test right now (since I only have one 3DS as of right now), but if I do get another one I can take a look at that some time.
The system the Mii was made on is determined by a set of bytes
near(?) the front of the Mii.
For Streetpass Special Mii†, it tends to be 00000000 or something like that.
The easiest way to make the system think it made the Mii, currently, is to make a new regular Mii, then extract the extdata, use HxD or your favourite hex editor copy the system bytes from the new Mii to the Personal Mii, then fix the checksum using your preferred method.
I'm pretty sure I'm missing important steps, possible decompression and recompression…
Been a while since I altered my Miis at all…
†Miis that are sent over SpotPass by Nintendo of given region. There are some Special Miis acquired not by SpotPass, but by special QR codes, or passing the a Special Mii's native system. Non-SpotPass Miis acquired by actually Streetpassing them, or using a QR code, do have System IDs. Special Miis acquired by by QR will never again be Special on a system that scans their QR code more than once, if that matters at all.
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EDIT:
Well, there's one of the very few advantages of a NNID, personal mii sync
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Given how you're forced to create one before any other Mii, I wouldn't be too surprised if your personal Mii is just the first one in the file, hmmmm
No. Your Personal Mii is identified a different way.
Overwriting the Personal Mii with any other Mii, even with a good checksum, crashes Mii Maker to home.