While there may not be any `visiting back and forth nonsense', you do realize that if you decided to leave Canada (even for a quick trip across the border) and you are denied re-entry, your application is toast, right?
You can apply for the OWP now, as long as you still have legal visitor status. It will take ~ 4 months to arrive. The form is IMM 5710 and the total fee is $155 +$100 for the `holder' fee/ money grab. Choose `initial work permit' and write `unknown' for the employer.