I used to do books, but I haven't done them in a while, so I tried a quickie test. I set up a facing-page doc with page numbers and 8 document pages, which I then changed to non-facing pages.
When I uncheck "Facing pages", the page numbers are on the left and right, and I want them on the right only.
Are you setting the text alignment for the page numbers to left on the left page of the spread, and right on the right page? If so, change them both to Away from Spine instead. For me, when I changed the document setup to non-facing pages, the page number for all pages was on the right side.
Also, the right side of the master spread won't apply to the second page (which are stacked instead of a spread.) I have to copy the elements from the master and paste them.
If you really want two different types of master page (such as you would have in a facing-page doc) in a non-facing page document, I can tell you how to do that, but I wonder if that's what you really want. I'm not sure if what I'm going to suggest is the best way, but it is a way to make it work.
In your master document, create two new non-facing master pages (in the New Master window, make the number of pages 1 to get a non-facing master). We can call the new masters B and C. Copy the contents of the left page of the facing-page master you already have (let's call it A) to one of the non-facing single masters (B), and the contents of the right master (A) to the other (C). After you change from facing pages to non-facing pages in Document Setup, the left page of the A spread will be applied to all of the document pages, which is why it looks the way it does.
Select all of the thumbnails of the document pages in the Pages pallet (click on the first, shift-click on the last) and go to Apply Master to Pages in the pallet's fly-out. Select B and apply it to all of the pages. While the document pages are still selected, do the same thing, but apply C to only the odd pages. You can do this by typing 1,3,5,7 (and keep going until you reach the last page of your document). The first step of applying B to all pages won't make the document look differently, since B looks the same as the left side of A. Also, the quicker way to apply B to all pages is to hold Option and click on the thumbnail for B. There is also probably an easier way to apply C to the even pages (like with a script), but typing the page numbers will work.
I hope that's helpful, but if I have misunderstood your question, please reply.
however sometimes our customers want them single-sided or want them in PDF (in which case I think it's best to design them as single-sided docs).
Facing pages PDFs are still exported as single pages under most circumstances. The exception is if you intentionally check the 'spreads' box in a PDF (Print) dialog from CS5 or newer, or if you export to PDF (Interactive) in CS5/5.5 using the defaults. In CS5/5.5 interactive PDF exports as spreads by default, and there is no option inthe dialog to change it, but there is a script that will toggle the setting on or off. See Interactive PDF from InDesign CS5 Always Has Spreads On | InDesignSecrets