Following up on this: I got @jim ms method working, although in a slightly modified form, as I ended up switching from PopupMenu to MenuItem (with .popup()) for other reasons. So I just made a new subclass of MenuItem with an override of MenuItem.Constructor(Text As String, Tag As Variant = Nil), as:
Public Sub Constructor(Text as String, tag as Variant = Nil, hovertext as string = "")
// Constructor(Text As String, Tag As Variant = Nil) -- From MenuItem
declare sub setToolTip lib "AppKit" selector "setToolTip:" (obj as ptr, tip as CFStringRef)
Works like a charm. I see the tool tip when I hover on the Menu Item, just like I wanted. Thanks a bunch for this idea, Jim!