Depending on how authentically Japanese, and how traditional Logan is after, Budoshin may not be the best match. Essentially, it's a modern American system based primarily on Judo with a few extra joint lock methods thrown in. Their history pages are rather a poor indication of quality, honestly, trying to associate themselves with a range of systems that have no real connection to their approach (most notably reference to Takagi Oriuemon "Shigenbudo", founder of "Yoshin Ryu"... er, no. Takagi Oriuemon is given the title/name Shigenobu, not Shigenbudo, and only within his Ryu-ha, which is not the Yoshin Ryu, but the Takagi Ryu. Although many lines of the Takagi Ryu also use the term "Yoshin", it does not make it Yoshin Ryu, as that name refers to a completely unrelated group of arts, known as the Akiyama Yoshin lineages. It's this line that lead towards Tenshin Shinyo Ryu, not the Takagi Ryu lines as the Budoshin website states).
In short, it's not traditional or Japanese Jujutsu, and has some highly suspect takes on history. That isn't saying it isn't good (I'm not stating my opinion of what I've seen of it here), just that it may not be what Logan is after.
