4. To qualify to HCP (targeted job offers) you do NOT need LMIA. You just need a permanent job offer in ANY job.i know the pain
Not sure if these options might work, but its a worth a try
1.Vigorously try for a job offer in Toronto , if you are in IT industry, try doing certificates like PMP , CBAP,CSM
2.If you are in the US , try for a full time job in US and persuade the company to work remotely from Canada.There are PEO companies in Canada which will take care of working remotely
3.Try for an intra company transfer