"Besides, I really don't think this proposed book is going to turn a profit anyway."

Well, while many if not most books are published for profit, a good number are not. For instance, my "proposed book" (presently in the process of layout) is in this non-profit category and I will be happy if I get my money back. There are many other reasons besides profit to publish a book. On the other hand my first book was for profit, but those were different times, before Internet.

And to address the original question. I had similar problems, and it took a lot of time - and nerves - to solve them. One major picure source, a prominent European auction house, flatly denied the use of their photos in my book. Many others just did not answer at all. But fortunately a number of other prominent auction houses gave me a permission to use their material (with proper credit, needless to say). And I also organized shooting of original photos expressly for my book, which took a lot of effort not to mention years of time ... In retrospect, I'm inclined to say that writing the book was the easy part.

Cheers,
Jani