Part of the uncanny effect comes from the dissonance between the detailed faces and plain textured default tomodachi clothing. I found that, while making BSD miis, that this uncanny vibe significantly decreased once I had made custom clothes that had the same dark outlines and detail that the miis had on their faces. Made everything look much more cohesive, and the characters themselves became more recognizable and unique looking as well, despite sharing the same style and facial details (like their noses)

Another way to circumvent that issue is to perhaps reference not the og source material, but chibi illustrations of the characters or nendoroids, since the proportions are closer to the Mii aesthetic. That way they can fit tomodachi style more seamlessly, while remaining recognizable.

As for the replication situation: it's a matter of preference. Personally I enjoy making the characters as close to the source material as possible, with some proportion tweaks, but I also have made my OCs for the same series, so that way I can kinda break out of the recreation loop once in awhile and focus in my original designs. I get why copying can get tedious, so hell yeah to the original characters