Aiken note heads: Are there thin variants with more interior white space for whole and half notes?

[Karlin High]

A songwriter asked me to type up some of her compositions. Much of the 
intended audience is in communities that have standardized on Aiken-head 
notes for most of the past century, and use little else. LilyPond has 
those shapes, no problem, I thought. But her benchmark is a certain 
publishing house that uses Finale with a customized font, example at 
this link:

http://www.prairieviewpress.com/images/pdfs/Kneel_At_The_Cross.pdf

I've been able to accommodate several of her requests for appearance 
changes. But for her taste, the LilyPond 2.19.59 whole and half notes 
have too little white space on the note head interiors. Apparently I'm 
working under the expectation that unfilled shaped-note heads be drawn 
with a thin, uniform line instead of horizontal lines being heavier. I 
got closer to her ideal by increasing NoteHead.font-size but expect it's 
possible to do more. Such as fiddling with MetaFont sources, if need be. 
Before digging in at that level, I did some Googling and found that 
topics like this have been discussed in the past...

https://code.google.com/archive/p/lilypond/issues/602

...and the 2.19 change log also metions something:

"Improved visual spacing of small and regular ‘MI’ Funk and Walker 
noteheads so they are now the same width as other shaped notes in their 
respective sets. SOL noteheads are also now visually improved when used 
with both the normal Aiken and Sacred Harp heads, as well as with the 
thin variants."
http://lilypond.org/doc/v2.19/Documentation/changes/index

"Thin variants!" I keep seeing that term. What are they, and how would I 
access them? Maybe I don't need to head for the new-to-me frontiers of 
MetaFont after all.
--
Karlin High
Missouri, USA