Shin's single status should actually be more problematic to Ei Sei.
One of my major gripes with Hara is that he's pretty much dropped the vast majority of political dynamics and intrigue from the story.
If he hadn't, the story would rightfully be treating Shin as the political entity he is: a renowned general at the head of a powerful army known and feared across all of China. More importantly, he is a sworn sword and ally to the king, to whom he owes his name, lands and titles (and probably a city by now, if Hara still cared). His descendants will presumably grow up up deeply loyal to the royal family and dedicate generations in their service.
To that end, Sei should be the one pressuring Shin to marry the most at this point. Realistically, Shin should be a highly desirable candidate for marriage, and it would make sense of Sei to use that to his advantage politically - to match Shin with an eligible daughter of a reputable family, perhaps one formerly aligned with Ryuu Fui or whoever - hell, perhaps it's Sei Kyou's widow, I could easily see a story line where she's being pressured to marry and it being Ei Sei's idea to arrange her into marriage of convenience with Shin.