Hi,
Can you apply for express entry under the BC PNP? There are threads on here showing they process those quickly, approx 1 month.
If not take a look around on here it looks like the grad category is the next fastest to process after EE.
If your WP expires April 30, you will likely get implied status until end of June/early July, apply by paper on April 25 or 26.
You may need to stop working for a few weeks if you are refused until your PNP comes through.
Once refused you will have 90 days to apply for something else or leave Canada.
Simply pay your $200 restoration fee and then apply online for a visitor visa (takes approx 1 month)
By then you should have your PNP and will hopefully not had too much time off work (I have had 10 weeks so far)