Your lawyer is correct on one important point: you cannot submit an H&C application while you have a pending refugee claim.
But based on what you described, it sounds like you have received a PFL and responded to it, but you have not yet received a final C-12 ineligibility decision. Those are different procedural stages.
I would not withdraw the refugee claim simply to file an H&C application without getting specific advice about the consequences. The more useful question right now may be what can be prepared while you wait, and what options become available if IRCC ultimately issues a final ineligibility decision.