I haven't seen much of Bill Bailey's character yet so I couldn't say.
Yeah, I agree with most of those. Although, I think Daisy is more extraverted and probably an ENFJ. But the procrastination makes me think ENFP. I think Tim could be INFJ though too, with his stubbornness at times and his dream to be a graphic artist. Brian seems to be more a feeler, so an ISFP, which is the artist type as well. I love this show! Too bad there's only two seasons.
For me he was always more F. Claudius survives by reacting in an appropriate way to thoughts and wishes of others. Sometimes he has to do it on the spot - e.g. with Caligula after his illness or after the dance. That's not the thing of INTPs I know IRL. Neither is agreeing with something absurd and then being quiet about it.