Hey Brian,
attached is a scene file of pretty much an MPM cloth setup from scratch (see scene file in ZIP).
The only thing I changed was modeling a different poncho shape assuring that the neck opening of the poncho fit tighter around the subject's neck. My Vertex color paint application was more conservative and went all around the neck and was smoothed out (see the attached image in the zip). The cloth sits up and off the model because all the Detail Size and Detail Size Scale are at their defaults. You could refine it by setting the Detail Size Scale on the solver_settings node to a lower value like .4 or .3 (this will be a slower calculation).
I did assure that the constraint was checked to use the color property and I had to increase the constraint nodes strength from 1 to 3.
As we see in the attached video (in the zip as well) the response is improved but could be taken further because again, most of the MPM settings are at their defaults. You could try lowering the inherit velocity on the collider but lowering this too much may cause the arms to pop through the poncho.
I think better modeling of the poncho will be key and a more sparingly use of color weight to control the constraint will help as well. Let us know if this helps.
You could also post the ABC file on here (if you can share it that is) and others may be able to give further guidance. There are a host of other settings that could be adjusted to give a better response.