Just a friendly reminder. I just booked travel from near St. Louis to KC for my wife on Amtrak for $29 one way. Station is a VERY short cab ride away from Kemper.
For those still needing a hotel, you might try Priceline. The last two years my wife submitted bids for four star hotels that were accepted, that were below the rate available at a Comfort Inn not far away. The Hotel Phillip must be all about the atmosphere, and I wasn't that impressed but it was cheaper and just as convenient. The Sheraton, or Hyatt, or whatever it was then was a bargain, convenient, and more comfortable.
Best Western on Southwest Boulevard and Rainbow has a shuttle that runs from 7 am to 11:30 pm and will take you to and from the Royal. You can always get a cheap cab back if you want to stay later.