After a bit of experimentation, and thanks to a script from http://www.howtocreate.co.uk that snifs out Opera no matter how it has set itself to be recognized, I managed to come up with a little script that hides the iFrame when the menus are displayed if the browser is Opera, and makes it visible again when the menus are hidden. I even managed to make my own add-in to DHTML Menu Builder so that my script is part of the menu’s generated code.
And it works! And there was much rejoicing!
Now Opera users get to see and use the menus, and I’ve added a nice little “complain to Opera if you don’t like it message.”