The author of the passage that I want to use as an epigraph keeps making references to sections of Herodotus’ histories, which, whilst I respect it, doesn't look good in an epigraph. Since I already indicate where I got the quote from, am I allowed to remove the in-text citations?
An epigraph commonly doesn't follow the conventions of scientific citation. Many epigraphs don't even mention the title of the work they are taken from, only the author. Or only the title, and not the author.
For example, here is the epigraph from the first edition of Mary Shelley's Frankenstein:
Did I request thee, Maker, from my clay
To mould me man? Did I solicit thee
From darkness to promote me?—————
Paradise Lost.
And here is the one from To Kill a Mockingbird by Harper Lee:
Lawyers, I suppose, where children once.
Charles Lamb
This incomplete citation is acceptable because an epigraph is normally taken from a source that the readers of the present work are familiar with.
I don't remember seeing an epigraph that itself contains references to sources, and I don't think I have ever seen one that contains ellipses or additions in square brackets.
The passage you quote is a summary of another text and provides an interpretation of it. That is not typically what an epigraph does. An epigraph quotes a well-known passage from a famous work whose meaning is obvious to everyone familiar with it. In your case, the epigraph should be a passage from Herodotus. Like this:
It is not therefore to be supposed that anyone,
except a madman, would turn such things to ridicule.
—— Herodotus
Which passage you choose will of course depend on the meaning you want to evoke.