Is there any other way of accomplishing these changes?
Yes, you can take advantage of Section 51 of the Income Tax Act and exchange your common shares for special shares in the company. It is a form of freeze but does not involve filing articles of amendment. It can only be used by the same company i.e. can’t transfer shares to a holding company and there is no limitation period to stop CRA from reviewing the transaction at any time in the future. However, it is very useful ion converting an equity shareholder to a debt shareholder (common for special shares).