Problem is though, the OS needs to be up and running for this to work. Any game or demo that takes over the system won't work.
Nope, you're wrong. If you set DISPLAYCHAIN=NO in the Picasso96 monitor icon then it'll work, because the Workbench will still be displayed even if it's the AGA output which is the active "screen".
Take my word for it, I've tried it myself :-)