H-1B visa, Canada and Finance(IB/RE)

I have a Master's Degree and 5 years of work experience (in construction industry) in the US and now I intend to pivot into a different industry through MBA. But the caveat is that I would have about 2.5 years of H-1B visa remaining after I graduate from a college in USA. No OPT left. The pros are that I do not go into any kind of lottery since I already have the visa. The con is that I have essentially no OPT and which means that my employer has to sponsor my H-1B visa and not only that but soon enough (probably within 1 year's time) file for my green card which means the employers will have to shell out even more money which would be required to sponsor my green card petition. 

Having said this, if I end up in a mediocre University like Fordham or Rutgers or Carroll(BC) for MBA, do you think that smaller boutiques or MM banks or Real Estate (finance role) firms (since I have construction management exp.) be willing to hire me and sponsor visas for me?? I have heard a lot about the visa sponsorship issues but the advantage with me is that after hiring me, I would be the one international who can work for the firm 100% without the issues and uncertainty around the visa lottery system. Would firms be interested in sponsoring visas for such a case coming out of mediocre universities??

Also, if I end up getting admits from a Rotman or Schulich or Sauder in Canada, along with the above universities in USA, which would be a wiser decision, to study in Canada since they have an easier immigration system in place or USA?? Hands down USA has more opportunities but what's your take on Canada?? Are the universities I mentioned above any good?? Is the finance/RE industry thriving there?? Are there any good opportunities in Canada?? Is it worth picking over USA??