Hi Jonathan
No superior knowledge I'm afraid

From experience, I'd say that you can't stick to one spelling, because you'll miss something or get led up the garden path. I have Clark's [without the e] but that doesn't stop even the occasional "official" document sprouting an "e", so a name like Hayes / Heyes / Hays even if it was spelled out, might be problematic.
Then you also have the transcription from the original to the copies & then to the index

You have to hope that her father has a reasonably unusual name, occupation or that they come from & stay in a small area

Best of luck
SandraC