Playing with track Weight may allow quick solving convergence, while keeping some (all) poor quality tracks.
Solve as usual, then run this script into a python console, and then solve again. Desired error is the wanted residual solve error. Nearly magic, for use with many tracks detected automatically. See this treadgithub repository for an addon version.
desired_error = 0.05
for clip in bpy.data.movieclips:
for track in clip.tracking.tracks:
track.weight = desired_error/(track.average_error/track.weight)