The wrong active set selection can be a problem also when we perform polishing to get high accuracy solutions (see Section 4 of the OSQP paper). I wonder if something similar to your LSQR step could be applied to the polishing phase to find a search direction for the high accuracy solution.
I am still not sure why it happens but the LSQR approach you summarized here https://github.com/oxfordcontrol/osqpth/pull/5#issuecomment-523942406 is quite interesting.
The wrong active set selection can be a problem also when we perform polishing to get high accuracy solutions (see Section 4 of the OSQP paper). I wonder if something similar to your LSQR step could be applied to the polishing phase to find a search direction for the high accuracy solution.