I know that this isn't what OP asked but in a similar situation I'd try to see if you can do a short hop MR for cheaper than doing that ORD routing. E.g. on the 27th you can fly PHX and back from LAS on US for $179, I'm pretty sure that nets lower than the ORD routing and uses probably almost the same amount of time.
I mean it's the holidays and you might not want to do that though... just an idea.