Slightly off-topic, but a friend has a signed Sadamune which they sent off to the NBTHK for shinsa. It was sent back 'horyu' because allegedly the panel had never seen a legitimate Mei to compare it with, and thus felt unable to authenticate it.
Subsequently this friend had the Sadamune Mei erased, and then sent it off again for shinsa. This time it came back attributed to, yes, 'Sadamune'.
By now they had found an old meikan entry with a photo of the same blade, with Mei, but as they had by then registered the sword as unsigned, they ended up in some kind of a Catch 22 bind.
(Any factual errors in the story above will be from my failing hearing and lack of ability to follow high-speed explanantions in Japanese! )
PS I know very little about Soshu and look forward to reading the articles linked by the OP (Brett) above. Thank you.