First, check the loads on the flight you want. Then try LAX UA 1K suggestion about same day change. Second, when you land @ ORD (though not sure if counters are open that late) ask that they to rebook you on flite #2.

And lastly, if the loads look good for flight #2, you could just show up for that flight and take your chances. Having done this a fair amount (20+ times) at ORD, both unintentionally (overslept) and intentionally (overslept) it certainly can work. Fatter fares and empty flights are the two variables to use for evaluation. Your 1P will make it happen if the equation works.

Oh ... and not checking any bags will make it easier too. Good luck! I'd say you'll find a way onto plane #2.