In the context of your 'question', beware of the path.
Nonetheless, regarding the content, the following comes through:
... two scholarly books self-published ...
Self-published or otherwise, there are two fundamentals: what is scholarly and what are scholarly books.
Irrespective of many opinions, a fundamental remains that scholarly pertains to academic and research. The elements, amongst others, are validity, reliability, rigour, ethics.
These are what reviews ought to safeguard.
Scholarly books ought to have these at their core, however in different shades unlike articles.
Scholarly books can also be books for teaching discipline subjects or can simply be monologue of collections. Are they scholarly, well they are. Do they extend/contribute to knowledge, they might. Would they be scholarly in the context of validity, reliability, rigour, ethics ...; That would comes through like a ... the proof is in the pudding
republishing more parts of my self-published books
I'll say, explicitly so, what you are republishing (as an article) cannot and shouldn't be those parts of your self-published books that were "previously been published in peer-reviewed journals".
If however any of these previously been published in peer-reviewed journals is/are to be republished, the word and the process is not that of 'republishing' but rather of publishing through the manuscript, review, publish process.
does this implicitly indicate to the reader/buyer that the books have somehow been peer-reviewed
First thing first, it is either it's been peer-reviewed or it's not been peer-reviewed. There's no 'somehow'
Secondly, it must be pointed out that peer-reviewed referred to the 'object' and not the 'form'. So, if the book and the chapters are not peer-reviewed as a collective entity, then it's not peer-reviewed. It's that simple. It's immaterial if post book chapters are peer-reviewed afterwards, it's immaterial in so far as the 'peer-reviewness' of the book itself is concerned. The post publication actions do not validate the already published book. It is inconsequential and nullity, as would be said in law; regarding the peer-reviewed
Do these in any ways improve the significance of my self-published books...
I'll say emphatically NO
Nonetheless, I'll still say, significance here is subjective. In any case, in the context of your 'content', the focus should shift to
- are others referring to the books and/or its chapters
- are the books being embraced
- are the books being scholarly engaged; whether critique, critic, complement, reconstructive, progressive...
- are works been derived from the books by others apart from yourself