They don't disappear when you edit the menus. There are items in the menu when in editing mode which will turn into the list of presets in normal mode. You can copy or move those items to anywhere you like to move the lists around.
As well as the automatic lists of all presets (or just presets within a specified category), you can also make standalone buttons for individual presets.
See the pinned post at the top of the Rename Presets are of the forum for more detail: