OK, I downloaded a new version of the cloner trial so I could try it on a different server. Everything works fine from within Joomla.
It turns out that jos_captcha_session was left over from a component that was removed 2 months ago, so I just deleted the file.
Back to trying to automate the cloner under Windows. The first mistake was that it seems you can't run a php script directly under windows. I did some research and tried the following command:
C:\...\php.exe -f C:\...\com_cloner\cloner.cron.php
When I modified Scheduled Tasks with the above command (and full paths

), Event Viewer showed that the script logged in and logged out after about 5 minutes but no backup appeared.
I tried running it from the command line and got the following error message:
"The encoded file C:\...\com_cloner\cloner.cron.php is not permissioned for this server."
I found this interesting since I had no problems running the clone from within Joomla.
In both of the above cases, the script was run with full administrator privileges, so privileges shouldn't be a problem. Any suggestions on what to try next?