I believe you have passed eligibility in GCMS notes; that's why they have asked for additional documents. You don't need the LIMA for BOWP. Just check there is "No" in front of "Restriction on Employment". If that is so, you are eligible for BOWP. Definitely apply before your previous permit expires. If you apply before the expiry, you will go on implied status while your BOWP application is being processed; meaning you can work as usual until the decision is made. In the worst case, if the BOWP application gets rejected, it will take 4 months and by then you should be done with your PR.
Since you don't have much time, do not go to the border for BOWP. You risk not being allowed re-entry in the country.
Check both of these links:
http://www.cic.gc.ca/english/resources/tools/temp/work/prov/bridging.asp
http://www.cic.gc.ca/english/work/permit/extend/permanent.asp