First of all, I appreciate your reply.It is in your best interest to apply for US Visa and then go to Canada via the land border. Since you are already a PR, you are legally allowed to enter Canada i.e the border officers cannot deny you entry. This means you will most definitely make it in time for your University. There are a few things you might have to worry about to make your case even more so in your favour -- read have your H&C reasons approved -- however you will without a doubt be allowed to enter the country, to have that reiterated. If you want more details on this, just let me know. I can provide a full write up on the process. I have myself gone through this process. Further, I have also consulted a lawyer for my case, and albeit that by no means means I am a substitute for a lawyer however I can hopefully give a general insight into the process.
The reason why I applied PR renewal before PRTD, is to successfully get my PR renewed and when I will be asked to pick up my card, it will be easy for me to get PRTD right away.
I would like to hear your side of story and how did it go for you.