I seem to recall the old cloth had a collison distance setting, but I can't find that in the cloth or deflector settings for the new cloth.

Is there a way to reduce that "avoidance" distance? It seems to be an absolute distance because scaling my model larger makes the relative gap appear smaller.

The setting you seek is called "Collision Tolerance", and it is set from the Choreography. (See screen capture)
Click to view attachment

thanks. Does that parameter mean anything like cm?

I believe it uses what ever units you have set. Possibly?

like almost all the plugins, it is in centimeters.