I had been doing internship with this company for years, since my sophomore year and my OPT so the only question she asked was "what do I do?" and that is it. I had more than ten I20s showing that.

I don't know how it is for contractual employees, for my company, I was the first H1B they ever did in their third decade of business.

You can just go to Canadian consular at Buffalo, or any other border, if you qualify they will give you the visa in a couple of hours to enter canada.

To get US visa appointment in canada, you can go to nvars.com.

Hope it helps