Should the Government or York Order Striking Workers to Vote on the Employer's Offer?

I noted that the Federal government has ordered a vote of striking transit workers in Ottawa. The employees will be required to vote on the employer’s last offer. The union had refused to take the offer to the employees because they believed it to be inadequate. The Ottawa transit workers are governed by Federal law, so the it is the Canada Labour Code that applies. The Code gives the Minister of Labour the authority to order a ratification vote in the public interest (section 108.1).
The same right exists under Ontario law. For example, Section 41 of the Ontario Labour Relations Act allows the Minister of Labour to order striking workers at York to vote on York’s final offer. Also, Section 42 gives the employer the right to order employees to vote on its last offer, but only once. Employers and governments use these provisions when they sense that there is dissension in the union ranks, or a disagreement between union executives and the membership. Therefore, if York believed that CUPE’s bargaining committee is prolonging the strike against the wishes of the actual striking workers, or that the strikers are getting tired of the strike, it could apply to the government to force a vote on its last offer. If a majority vote to accept that offer, the strike would immediately end.
Do you think York should try this?