Beyond the microphone being high impedance (60K-100K?), and push to
talk, I'm not sure what I need to be looking for (or avoiding) when
looking through a current catalog of available microphones

Paul-

As I recall, the HW/SB-100 series of radios had a reputation for good audio. I
tried several hand-held microphones with mine but found the beige or green
Heath ceramic microphones to be as good as any. I believe they were a Turner
microphone with the Heath logo attached.

The Shure magnetic (controlled reluctance) microphones may have higher output
than the ceramic microphones, but I recall receiving reports of "bassy" audio.
If you want to try one, look for a Shure 404C. (The 404B is low impedance and
would work with the more modern rigs.)

Over the years I have had many more failures of microphone cords at points
where they enter the microphone or the connector, than failures of the element.
I trust you have checked your cord.

One factor you should keep in mind, is that it is possible to introduce a
"ground loop" by connecting the microphone shield to the push-to-talk return
wire inside the microphone. To keep extraneous power supply noise from being
injected into the microphone amplifier, make sure there is a separate lead for
the push-to-talk return and the microphone shield. Even though they may be
connected together in the connector, a common wire inside the cord is enough to
couple noise to the microphone circuit.

73, Fred, K4DII