Agree, don't mix up the two issues of 1) getting the visa with 2) traveling on the visa. These days, #1 is definitely the harder of the two. There is also some confusion on your part about visas. It sounds like you need to apply for a student visa (X1 or X2 depending on length of your study course). Your university should give you the correct documentation to do that. You cannot get a tourist L visa then convert it to a student X visa in China. You may be confusing this with something else, see a couple of paragraphs below.
I did not think that for X visas, any evidence of international tickets in/out of China was required. Just the application form and the correct paperwork from your school. So check the application requirements first for Student Visas wherever you are going to apply. If they confirm that you don't need to provide any air tickets in/out, then that is a major hassle averted. Normally you would fill out the application as if you are studying the entire time in Shanghai--certainly don't mention plans to enter at or visit Xinjiang.
Now for the part you may not realize: while you can travel through and around China (except Tibet) on an X student visa, there are some timing issues. If you are getting an X1 visa (study period > 6 months) then that will have to be converted to a Residence Permit within 30 days after you arrive in China. The RP will then function as a multiple entry visa for however long they issue it for. The problem for you is that it can take up to 3 weeks to process an RP including the medical exam. So you really need to get to Shanghai as soon as possible after you enter China, so this process can start, with the school's assistance. They will have your passport for some to all of that processing time period, so you would not be able to travel very far from Shanghai.
If your time period is short term (< 6 months) then you'll be getting an X2 visa which is normally single entry but good for the duration of your study period. These are not converted to Residence Permits and therefore a lot less hassle up front since there is no process other than entering China, at which point you can travel around within China, until you need to show up and register at the university. You would not be able to exit and re-enter China if it is the standard single-entry.
Note that your X visa may be issued with dates that do not allow you a long period of time in China before you start official studies. I therefore suggest that you go through the application process and see what you get, then finalize your plans to enter and get to Shanghai. I have a feeling you are not going to have time for the Grand Tour of China that you expect to have.