How can I use the browser as a UI for a desktop app? The ways I have come up with so far are...
You did not mention the OS you will need to target. But you might be able to create a program statared web server, then launced the default browser. Wait until the browser is terminated by the user and then shut down the web server.
So for example on windows you can use CreateProcess() to spawn the process then MsgWaitForMultipleObjects() to wait until it is finished executing.