Is there a way to prevent tied notes from triggering multiple note names with \context NoteNames?

[Matthew Probst]

I've been using Lilypond to create lead sheets for a band that I'm in, and
it works great for that.  Between that and a website I use for generating
simple chord charts, we're covered for our notation purposes.

I have some less skilled note readers in the band--they can read rhythm
notation, and get a general idea of melody shape from the notes on the
staff, but things go easier if they can see the note names for each note
under the staff.  That's easy with LilyPond:

LeadStaffWithNoteNames = \new Staff \with {
instrumentName = #"Lead (notes)"
}
{
    <<
        \relative c'' {
            \HomeKey
            \clef treble
            \LeadIntroFull
            \LeadHeadFull
   }
   \context NoteNames {
            \set printOctaveNames = ##f
            \LeadIntroFull
            \LeadHeadFull
   }
    >>
}

This works great, except for one cosmetic issue:  For tied notes, the note
name is repeated for the second, third, etc. tied note.  While my weaker
note-readers can comprehend this given that they can grasp the rhythmic
notation, it's a bit of a hassle.

Is there any good way to automate printing of note names underneath the
staff while avoiding repetitions of the note name during ties?  I did a
search of the snippets repository and the documentation for Lilypond
2.22.0, which I'm using.  I'm guessing that it might require custom Scheme
instead of just configuration parameters, but I might be wrong.  I know
Scheme the language and Lilypond the markup language, but not Lilypond the
Scheme API.  I'm willing to do lifting on the code myself but would welcome
pointers on how might be best to accomplish it. so I can best direct my
learning.