I found a way to do it!! I found a way to authorize two different Audible 'marketplaces' (as Audible calls them) in Books.
Someone at Apple explained that, because I'm in Canada, all the Apple apps like Books, App Store and Music will only take me to Canadian websites. So I'll always land in Audible.ca when I click the 'do you want to authorize this account' button.
After making absolutely sure that my Audible.ca account was authorized, and my computer could play my .ca titles, I changed my default browser from Safari to Chrome, and I signed into Audible.com on Chrome.
In Books, I clicked on one of the .com titles I had already downloaded, and I got that little window asking if I want to authorize whatever-it-is (Audible account?). That link took me, of course, to Audible.ca's 'do-you-want-to-play-this-in-iTunes' page.
So I edited the URL: I changed .ca to .com ... and I hit return.
That took me to the exact equivalent page on Audible.com. (I was pleasantly astonished that it had worked!)
I clicked on the orange button ... and got some supplementary little window asking if I wanted to play the file in, of all things, Music. I said yes.
And I could play my Audible.com titles in Books!
Now, I don't know what I had done in the meantime, but I could no longer play my Audible.ca titles in Books, even though nothing had been de-authorized. Clicking on the orange 'play in iTunes' button on Audible.ca only got me a message saying it didn't work. .... sigh ....
In another Apple support chat, the support person asked if I had tried re-downloading the books. I hadn't, but that's what I had to do -- delete, re-download and re-import every single Audible.ca purchase.
But I can now play -- and sync with my iPad -- downloads from both Audible.com and Audible.ca.
