Nevermind, I got it figured out. In case anyone else needs to know, the syntax is similar to this:
[vba]
Sub AddNewMenu()
Dim cWindowMenu As CommandBarControl
Dim NewMenu As CommandBarPopup
Dim menuItem As CommandBarButton
Dim subItem As CommandBarPopup

'delete the menu if it already exists
Call DeleteNewMenu

'find the (Tools) Menu
Set cWindowMenu = CommandBars(1).FindControl(Id:=30009) 'id = Window menu - we will put it before (to the left) of that

If cWindowMenu Is Nothing Then
'add the menu to the end
Set NewMenu = CommandBars(1).Controls.Add(Type:=msoControlPopup, temporary:=True)
Else
'add the menu before the Window menu
'Set NewMenu = CommandBars(1).Controls.Add(Type:=msoControlButtonDropdown, before:=cToolsMenu.Index, temporary:=True)
Set NewMenu = CommandBars(1).Controls.Add(Type:=msoControlPopup, before:=cWindowMenu.Index, temporary:=True)
End If

'add a caption for the menu
NewMenu.Caption = "(Tombstones)"

'1st menu item
Set subItem = NewMenu.Controls.Add(Type:=msoControlPopup)
With subItem
.Caption = "Normal"
Set menuItem = subItem.Controls.Add(Type:=msoControlButton)
With menuItem
.Caption = "1st"
End With
Set menuItem = subItem.Controls.Add(Type:=msoControlButton)
With menuItem
.Caption = "2nd"
End With
Set menuItem = subItem.Controls.Add(Type:=msoControlButton)
With menuItem
.Caption = "3rd"
End With
End With
'2nd menu item
Set subItem = NewMenu.Controls.Add(Type:=msoControlPopup)
With subItem
.Caption = "With PM"
End With
End Sub
[/vba]