I feel like House Liam's bad reputation is sorta at odds with the changelings' medieval aesthetic. If you want the Whole Medieval Vibe, you do need to have some Respected Clergy hanging around.
I'm not totally sure how I'd fix them just yet, but I think I'd start by changing them from House Liam into the Order of Saint Liam. They're respected by many seelie fae; not so much by unseelie fae.
I would have the story go that King Liam felt that Christianity's teachings on kindness, charity, etc., complemented the Seelie way, and so he syncretized them into fae philosophy. The story would say that he appreciated the Church for its work in keeping records and preserving literature, and decided to found his own order.
Members of the Order of Saint Liam are usually pretty sincere about that kindness and charity stuff, but they also heavily lean Traditionalist. Like, they believe childlings should never go hungry, but they also believe that monarchy is innately good.
And of course, there's corrupt members and members who secretly practice forbidden Arts, because the whole thing wouldn't be complete without them!
