Why cant your spouse sponsor you? You can work from usa any number of years even if you are a canadian PR but you have to stay in canada for 3 years within a 5 year period to maintain PR status.
The requirements for TN are laid out clearly. If you show up with a degree not matching job requirements or an inadequate TN letter then it's a guaranteed rejection. Some just show up with just an offer letter thinking it's a right of passage and are promptly sent back.
I drafted the letter...
Top US grad school wont help with GC. It will help with employment and then maybe a path to gc through employer but if you were born in india even that path is closed.