There's currently no way to do this system-wide. If you make the app you're using for the demo, you should consider making the app do the rotation for you.
Design the app so when it's in landscape mode it displays a portrait mode screen (ie, the app always appears rotated on its side). Then hold the ipad in landscape mode, turn rotation lock on so it stays that way, start your app, then use your app with the correct orientation. Turn your monitor on its side to see the faked portrait mode.
You can also do this for presentations if you turn all your slides on the side.
However there's currently no way to do this for apps not designed for it.