Under section 55 of the Supreme Court Act, the prerogative of reference to the Supreme Court belongs to the Governor General in Council alone. That doesn't mean, of course, that there could not be a resolution of the House of Commons recommending that the cabinet make that reference, but it of course would not be binding, and you could not refer directly.
Should you make that recommendation to the current cabinet? I don't see the point of it. The current cabinet knows that this is available and is either interested in proceeding according to the rule of law, as elaborated by the Supreme Court of Canada, or is interested in failing and maybe blaming or pushing.
I guess I think that this committee is not going to shape the exercise of that prerogative power of the cabinet of the Government of Canada.