Don,
Using your explanation, I would expect that setting the cursor to (15,0) and then starting to write my string, I would write 25 characters (1 visible and 24 'invisible') and the 26th would appear at position (0,1). However, my understanding is that using autoscroll or scrolldisplayleft moves the cursor position each time (i.e. after the print/write, the cursor goes to 16,0 but then gets decremented back to 15,0) so the 'wrap' should never happen.
In my case, it does wrap on the 27th character (haven't figured out where I lost 1 yet!), but starts at position (7,1). It would seem that the scrolling is not, in fact, changing the cursor position. I tried to do that explicitly (set the cursor to 15,0 each time I write) but that got me some other weirdness.
In searching for other solutions, I came across a number of posts that seem to indicate the 'scroll' functions often yield unexpected results. Also, there was mention that setcursor is really pointing to a memory location, and that sometimes that doesn't correspond to the physical display location you think it does.
Have you seen any of these phenomena before? Do you use the lcd library that ships with the Arduino IDE, or are there 'better' ones out there?