How is the wording weird? It clearly says OP can work until July 7th or the date application is processed, whichever comes first.
That said, the statement is contradictory to the current rule which does allow work under maintained status.
Get your employer to become designated in Atlantic Canada and then you can apply directly for PR. You can also get an OWP while waiting. If you haven't received an invitation in 2 years, it means your score is very low - French might help.
If everything else fails, just claim asylum. It will...
You can start working with new employer if both employers agree to keep you on payroll of first. Alternatively, you can quit and start new job after applying for work permit.