I found a decent work around. I added a non-breaking space to the end of each string and that was enough of a change to get copy, paste, and delete to show up in my context menu. The unicode character for a non-breaking space is 00A0. The syntax looks like this "\u00A0".

elementContextMenu = new ContextMenu();
elementContextMenu.hideBuiltInItems();
 
var cutItem:ContextMenuItem = new ContextMenuItem("Cut\u00A0");
var copyItem:ContextMenuItem = new ContextMenuItem("Copy\u00A0");
var pasteItem:ContextMenuItem = new ContextMenuItem("Paste\u00A0");
 
cutItem.addEventListener(ContextMenuEvent.MENU_ITEM_SELECT, onCutItem);
copyItem.addEventListener(ContextMenuEvent.MENU_ITEM_SELECT, onCopyItem);
pasteItem.addEventListener(ContextMenuEvent.MENU_ITEM_SELECT, onPasteItem);
 
elementContextMenu.customItems.push(cutItem);
elementContextMenu.customItems.push(copyItem);
elementContextMenu.customItems.push(pasteItem);
 
Application.application.contextMenu = elementContextMenu;