I've once had a hard seat in a fully booked train from Shanghai to Nanjing (and that was a slow one, so it took around 5hrs)... now, Shanghai to Xi'an is, of course, way longer, and might get you really on the edge of your nerves.

It will be crowded, not only from people, but also from luggage. It is definitely doable, as the Chinese train system, even in hard seats, is still way above Indians levels, but it won't be like European/NA rush hour. I suggest you're giving yourself a good dose of Tsingtao (or any other alcohol or you prefered, legal drug) to get yourself more relaxed. Also, such a distance should be overnight, no? Do you have hard sleeper, or really only hard seat? Hard sleeper is not that bad, yes it's full, but you'll eventually be able to sleep.... hard seats will make things harder...

I would consider looking around if you've to travel on those very dates... maybe there are still Business class seats available on Chinese Eastern? Should not cost a leg and an arm...

One other note, recently the Chinese gouvernment does try to limit travelling on National Holidays by splitting them into more but smaller periods. Might help a bit in your case, but probably won't help much.