Hell yeah! Alright, I think I have some good suggestions for you.

Moriarty the Patriot: a recent anime that turns the formula of Sherlock Holmes on its head, and has a lot of very intriguing characters.

Monster: A now classic anime about a doctor who saves the life of a man who goes on to become a serial killer. An extremely intense psychological thriller. This one DOES have some horror and gore but I think it’s safely in ‘Silence of the Lambs’ territory. Fair warning I also haven’t watched it in a long time so please make sure to check does the dog die for additional warnings!

Demon Detective Neuro Nōgami: a serial mystery anime about a crime solving demon. The mysteries themselves aren’t particularly interesting, but the psycho-sexual relationship between the demon and his human young lady partner/servant are something I think you’d enjoy.

for comedy anime (since you like golden girls and the nanny) both Ranma ½ and Urusei Yatsura are absolute classic sit-com anime. However the “situation” is pretty over the top in both. Ranma ½ is set in an over the top martial arts milieu, and Urusei Yatsura is about aliens invading 1980s japan. They both rely heavily on romantic comedy and drama.