Finally got my car registered. I can now confirm that they go off the sale price you write down on the title. I got an amazing deal on a car for about 50% of KBB value, and they didn't bat an eye. Starting to wish I'd gotten an even better deal, you know?

Side note - it is a lot easier to buy a gun than it is to register a used car. Ridiculous. The best part was paying the KS Highway Patrol $20 bucks for them to spend 30 seconds writing down the VIN under the hood. They didn't even look to see if the VINs on door jambs, etc. matched.
Second best part was paying the 50-cent "tax collection fee" on top of the taxes. JFC.