You might have a bit more luck on the east side of Monroe, just south of Regent St. I lived on Madison St between Garfield and Oakland until this past July, and that street, for one, is a mix of rental and owner-occupied housing from Garfield to Regent (with a decent skew toward owner-occupied). It was quiet (excepting football Saturdays, in which case it was usually the owner-occupied houses that were the loudest...no matter how old, UW alumni love their football), and you still have great access to Trader Joe's, etc, and a 35-minute walk to the Capitol, if you feel so inclined.
Check out
Tallard Apartments in addition to MPM. I think their rental base is centered in the Vilas Neighborhood, and I had a pretty decent experience in dealing with them for the year I rented there.