This is incorrect. Honor died shortly after the Recreance, which definitely happened after The False Desolation. I guess it's possible that there was a large spren similar to the proto-Nightwatcher and proto-Stormfather that was subsequently infused with one or several of the Rosharan Shard's essences, before being made into an Unmade. This idea makes some sense, and I believe it's somewhat mentioned in the newest Shardcast. Unless there's something im missing though, there isn't too much textual evidence for it as of yet.
As for the other Unmade having any relation to Shards other than Odium, there is an AMA from a few years back, where Brandon explicitly states that these Splinters of Odium. While this doesn't nessescarily mean that they aren't also infused with the investiture of other Shards, it does seem unlikely. Is it even possible to corrupt non-spren in the same way that was attempted with the Sibling? I do kinda like the idea overall though, Sja-Anat being something infused with Cultivation investiture hence the enlightening of spren, maybe Nergaoul being somehow related to the new Valor shard. I don't think this would be the case with all the Unmade though.