Two reviews of my book

As far as I can tell, two reviews of my book have appeared so far.
The first is by Stuart Rowlands and was published in the journal Science and Education. The review summarizes the book and makes links to those working in education. I was pleased with how well the author was able to relate the more obscure debates in philosophy that I talk about to questions in science education.
The second is by Juha Saatsi and appeared in the Notre Dame Philosophical Reviews. Juha and I have been working on these topics from somewhat different perspectives for quite a while, so I really appreciated his critical feedback on the book. I think it is fair to say that he is generally quite positive, although he raises a few objections at the end. The most substantial objection concerns my worries about explanatory indispensability arguments for realism about mathematical truth. I claim that plausible restrictions on inference to the best explanation (IBE) undermine these arguments. It is hard to find a good version of IBE that justifies interesting mathematical claims like that there are infinitely many primes.
Saatsi worries that my restrictions on IBE are too restricted:

Although I won't argue for this here, it seems to rule out typical IBEs that some scientific realists take to support our best high-level theories, because such theories can often be replaced with a weaker explanans the content of which falls much short of the theory as a whole. Even if such a replacement is quite arbitrary and unmotivated from the theory's perspective, for a sceptic who has not yet accepted the theory it is an epistemic possibility that only the weaker explanans is true. So, by Pincock's lights, the theory on the whole cannot enjoy any justification deriving from its explanatory success. This 'anti-holistic' viewpoint goes against the view that a theory -- the whole theory -- with appropriate theoretical virtues can enjoy a degree of confirmation by virtue of furnishing us with a good explanation.

This is a fair point that I would like to continue to work on. First, what is a plausible form of IBE and, second, what sort of scientific realism does it really warrant if it is does not warrant new beliefs in mathematical truths?