I think it would be better not to overstay. I know of someone who also found an employer but overstayed. In the process of the LMO application, she received a letter from CIC that she has been overstaying and has to leave Canada. You could always complete your application at your country of origin for a new work permit, while renewing your TRV as well.
Point of Entry applications are only for citizens of visa-exempt countries. Check out:
http://www.cic.gc.ca/english//visit/visas.asp, if your country of origin is on the list, then you're not eligible for application at the border. You might be eligible for application at your regional office though. Check CIC and inquire.