It's the thing that I want to do most often, but currently, when I hit menu while iTunes is open, I have to do a lot of scrolling and clicking to get the that playlist and then it doesn't even seem to play half the time when I select something in it.

I just want to play the iTunes DJ playlist right away. 

Right now, individual playlists, tracks or albums are not available as 
freely placeable menu items.

For what you want to do, you can, however add a custom action (and 
mark it "global", so that it becomes available as a menu item as well) 
with this AppleScript snippet:

tell application "iTunes" 
play (1st playlist whose name is "iTunes DJ") 
end tell

You can add custom actions at Prefs > Mapping > iTunes > Select 
"Custom actions…" from the drop down.

Best regards, 
Felix Schwarz 

What I had to do (did I do it right?) was pretend that I wanted to change a button behavior to a new custom action. This allowed me to create the actionscript as an item that could then be shown in the menu. Next, I changed the button I'd changed back to it's default.

Is that the only way to do that? It seemed non-intuitive to go to mapping (which is about buttons) in order to create a menu entry.

Thanks for the feedback!

Best regards, 
Felix Schwarz