You already have a fine list of other series, but, one I might suggest that I think would fit nicely for you would be the Mr. Wong detective series, starring Boris Karloff.
I suggest the The Falcon series, the Boston Blackie series, The Saint Series (which is just like the Falcon films). Some other series are Lone Wolf, and The Crime Doctor. All of these have been shown on TCM in the past and I'm sure will be again sometime.
There are the Dr. Kildare/Dr. Gillespie and Nancy Drew series as well as the Lionel Barrymore films "On Borrowed Time" and The Return of Peter Grimm". Also the films “Beyond Tomorrow”, “The Next Voice You Hear” and the original versions of “We’re No Angels” and “Angels In The Outfield”.