Hi Bruce, I totally understand the confusion! It does look like a wild coincidence, but in the Japanese sword-making tradition, this is actually a very structured practice called Shūmei (襲名, Succession of Names). It wasn’t a coincidence that two guys named Hosokawa used the same name/seal; it’s because they belonged to the same lineage. The WWII smith (7th Gen) was the direct professional descendant of the 1800s smith (1st/2nd Gen). In this culture, inheriting the "Brand Name" (Masayoshi) and the family "Seal" (Kokuin) was a way to show legitimacy and honor the founder.
As for your question regarding the specific Kanji in the Kokuin: as a native Chinese speaker, I would describe this as a highly stylised or artistic form of Zhuanshu (Seal Script). It is quite difficult to pinpoint the exact character it originates from just by looking at the strokes, though I suspect it could be "義" (Sometime the '我' part was written in a separate way, as the picture below shows). However, based on my experience with Chinese seal carving, the minor variations in detail you pointed out don't necessarily constitute a different character or identity. In this context, they are effectively the same Kokuin. Given that this functioned much like a Family Crest, it is not surprising at all that Masamori would use it even before officially inheriting the Masayoshi name.
Regarding the different form of writing the first Kanja of Hosokawa, the one has a '糸' on its side is a very ancient way of writing it in China. The '小' part was simplified into three dots sometimes, so it was consequently written as '細'. Therefore, they are the same Kanja in fact. However, when Japanese was being standardised during the Meiji Restoration, the '糸' version was designated as the sole official form, which is likely what caused this distinction.
Lastly, I've sent some messages to your facebook account about the Mantetsu survey (it was that survey led me to this post in fact), I'd appreciate it if you can have look whenever you are available.
https://meitou.info/index.php/細川正義#i8e2d584
https://tokka.biz/sword/masamori.html