Hi Barry,
unfortunately I do not have a ready-made solution - while it's possible to change the ambitus note heads to a single specific sign by issuing (for example) \override AmbitusNoteHead.style = #'do in the \layout block, this is not a solution since it changes both ambitus note heads at the same time -, I just want to point out an inherent problem:
As far as I understand, \sacredHarpHeads and \aikenHeads depend on the key signature chosen (in much the same way that movable do syllables do). So, it's a bit dodgy to issue ambitus information using these signs since the key signature might change in the course of the piece. (Strictly speaking, the ambitus signs occur at a place before a key signature is issued - but this slight inconsistency applies to ambitus marks in general since they show note heads *left* to the first clef ever encountered by the singer.)
Best
Lukas