Outside the enormous heaps of anachronism blending multiple historical systems of titles, I don't think there's anything unreconcilable between the two, although the application of the term Shogun for a mere Duke does stand out as a bit inappropriate linguistically. Besides being a military title that literally means "War Leader", it's a title that would presumably have supremacy over that of Gunji-no-Kanrei, which doesn't seem to be the case.
What you have is a blend of three distinct Japanese systems of noble titles: The original Imperial Court in Kyoto from the Heian through the Kamakura period, the system created by the Tokugawa Shogunate following the Sengoku era, & finally the Westernized peerage established by the restored Emperor Meiji.
Daimyo refers to the leader of a powerful independent military clan, that following the end of the Sengoku era was a direct vassal of the Shogun. The amount of land & authority they held was completely variable, ergo there were numerous categories of Daimyo. Tozama Daimyo refers to a Daimyo who's Clan was not an established ally of the Tokugawa, who typically held lands distant from the capital. Fudai Daimyo, on the other-hand, were the most trusted allies of the Shogun who were often assigned small plots of lands in strategically important locations.
Shishaku & Koshaku on the other hand, are Meiji era titles that most closely parallel what we see in Western nobility - the titles were created to be directly equivalent of Viscount & Marquis directly.
A Shugo was a local noble authority under the Shogun prior to the Sengoku period, most of which either consolidated their control & became Daimyo or were usurped & their lands absorbed.
Kuge referred to the Kyoto court's aristocracy as a whole, it is not a title.
While this is unofficial, I suggest the two tables be treated as complimentary as follows:
ATOW HBHK
Civil Title Military Courtesy Title
T1 Kuge -
T2 Lord/Lady Samurai
T3 Danshaku Fudai Daimyo
T4 Danshaku Shugo
T5 Shishaku Tozama Daimyo
T6 Hakushoku Tozama Daimyo
T7 Koshaku (侯爵) Daimyo
T8 Koshaku (公爵) Shogun
One is an official civil title of peerage. The other is an equivalent military courtesy title granted to a peer of appropriate rank. The noble in question as well as the speaker will of course emphasize whichever title better suits the situation & their personal priorities. We've already got a "They use both titles as the situation dictates" explanation from Handbook: House Kurita. Further extrapolating from that to bring some semblance of order to the overlapping application of titles doesn't seem like much of a stretch!
