Fallacy of this argument though: If ticketing for a specific train has already progressed to the point that you can't get all 4 tickets in the same compartment, then you are unlikely to be able to find availability of 4 lower berths either, at least not in the same train car. 4 uppers maybe, and that has less "trading value" of course. Underscore: importance of making prearrangements for sleeper tickets if you're on a short trip with essentially no time flexibility.

OP's trip is in August--which is a busy time for domestic travel in China since school and university students are still on vacation--so making advance arrangements for sleeper train tickets via hotel or 3rd party agent is important. My guess is that when he arrives in Beijing, seat tickets for the bullet train Xi'an-Beijing 6-7 days' hence will still be available for purchase, which can be done by himself.