I tried what you said and it works, but it's a little funky to set up.
I plugged in two identical joysticks and set up the profile for joystick1 and saved it. When I went to joystick2, it was already set to use the profile for joystick1 that I just finished. The button layout carried over, so I reconfigured it with player 2's inputs and saved under a different name. But then, the tab for joystick1 said that it was using profile2, and in reality it wasn't - both joysticks used their respective profiles.
So I unplugged both joysticks and then plugged in the one I had been using as joystick2 and it assumed profile1. When I plugged in joystick1, it assumed profile2. It looks like the profiles aren't tied to specific hardware but the profiles are loaded in order of creation. This will work perfectly for my needs, just plug in joy1 first, then joy2. Now if any guests are uncomfortable using the CP for a console emulator, they can use an actual joystick from that console.
Thanks for the help - Xpadder FTW!