You are not entitled to stay based on already having applied through CEC. You should start talking to the employer now about applying for an LMO for you.
When you are a graduate on a PGWP, you are already exempt from the hardest part of getting an LMO and that is showing recruitment efforts.
In cases where the employer is making a permanent job offer to employees who have completed the PGWPP for employment in a skilled occupation (within National Occupational Classification 0, A and B codes only), the employer will not be required to demonstrate recruitment efforts. It is recommended that the employer submit the application for an LMO approximately four months before the expiry of the Post-Graduation Work Permit.
Like other people here say, you could apply through PNP but the only thing that will do for you is allow you to get a work permit without needing an LMO. If the employer is not willing to apply for your LMO, he is probably not willing to sponsor you through PNP either.
Worst case scenario, if nothing works, you might have to go home in July and wait for your CEC or get your wife to sponsor you which may not be faster than CEC depending on where you come from. You could in July if you haven't applied for anything else apply to change your status to visitor but that means you can't work.
If you apply now outland for your wife to sponsor you and you come from a country with fast processing or you apply through the US, you could possibly have your PR by July. Once you have your PR, you can withdraw your CEC and you will at least get the right of PR fee back but processing fee only if they haven't yet started processing.
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