I was in the same situation and here's what I did as advised by my lawyer.
She asked me to send in a paper application for the BOWP. That takes longer and her hopes were that in the time it takes for them to get to my application, I would have received a positive assessment on my application (I hadn't yet submitted my PR). Once I got my provincial nomination from Ontario, I submitted my PR application but unfortunately, they got to my BOWP application by then and refused it because it had not passed the criteria. I was legally able to work for the 4 months between when my work permit expired and my BOWP was being processed. But now I can't work legally anymore and must apply to restore my status.
I'm not sure if this was the right way to go, but it worked in my case and had the PNP application not been delayed, I wouldn't be in need for a BOWP at all. I know of a few other people who took the same route and it worked out for them.