I'm thinking I'm probably extra stupid, but I kind of got the impression from the Event handling docs that if you wanted to send out your own events, you had to have your own events class. It seemed to me there was something magical in the constants defining event names in your events class that somehow made the events so named "your" events. It turns out that if you want to dispatch an event "this is an event" then it really is as simple as
dispatchEvent(new Event("this is an event"));
Then all you have to do is add an event listener for "this is an event". There's no more magic to it than that. The event just needs to be called the same thing on both sides, and that is what the constants make sure of. But they're not required.
Now, if you want to pass more information in an event, such as whether a click on a Multiple Choice Question is right or wrong, then you'd need your own Event class. But for simply broadcasting an event you know is yours, you just send out an event as above. Duh.
I figure most people reading this are not as "challenged" as I am, but hopefully this helps someone anyway.
Update 7/3/2008: When a component is dispatching events, it should also "announce" what events are available on it with an Event metadata tag, such as [Event (name="thisIsAnEvent" type="flash.events.Event")]. This allows you to use it in MXML without a compiler error. I honestly don't know whether multi-word event name, as stated in my original example, would cause an error or not.