How can I best approach journals and academics about paying to re-use content from their papers? Apologies if this is off-topic - please close away if it is. 

I am currently engaged in writing a book. This isn't speculative - I have a commission and an advance and a budget to spend on securing additional things required such as images and photographs. And the subject matter isn't the sort of new-age nonsense academics get occasionally pestered with during their careers.

Although it's not an academic text, one of the chapters is quite academic in nature, and discusses some niche topics in archaeology. I'd really like to secure some photographs of the finds in question: they're easy to track down online.

This question - I&#39;d like to use a figure from a paper; what&#39;s the best way to do this? - makes it clear that, as I suspected, I'd need permission (and like to pay a fee) to republish the photos. That's fine, and of course someone deserves remuneration for my profiting from their work. 

The trouble I've got is that no-one I've contacted seems the least interested in helping. I've mailed several journal editors and contributors alike, asking for permission and offering to pay, but I've had no responses at all.

I was once a PhD student myself, and I'm aware that many academics are disinterested in such relatively trivial requests. But I don't know what else to do: if I can't secure at least a few photos, the whole book is likely to be cancelled. Who am I best off approaching about this, and how am I best off approaching them to try and generate some interest and engagement?
Many journals have a "Request Permissions" feature on their website. Open the paper of interest and look for a button with that label - often it's grouped with other options like downloading citations, setting up alerts, etc. Then follow the instructions given.

Although I've seen this in a lot of the major journals in my field, I've not done an exhaustive survey of how many journals have this option, so your mileage may vary. But it should be a good first place to look. To take an example from your comment, the Bulletin of the American Schools of Oriental Research is on JSTOR, and if you visit the page of an article, there is a "Request Permissions" button right at the bottom, below the abstract. Example here - I hope that the link is stable. If not, visit the latest issue and open any article.