Because menu item editing doesn't use the editor shape composition as normal content editing, custom fields won't show up.
I don't know if Piotr's new version will support this, I know it has a lot of changes - but haven't heard anything for a while regarding when the new version will arrive.
I'm working on different module that will enable hugely customisable scenarios like this. Basically building any graph of arbitrary content relations and completely customising the templates - essentially you could completely replace the menu with your own
custom content types. I've got it working but it's not quite suitable for release :) I was going to post about it later.