Okay, it's running. I'm not quite sure exactly what finally did the trick - I played with modifying the access privileges, as one of the articles suggested, and I restarted the task, which I hadn't always done before, as well as fiddled again with some of the account settings. Maybe a task restart is also necesary when something changes, although I would expect it would make the attempt and fail each time, if it was a privilege issue. Otherwise, it would indicate that the task was storing the privileges it read on the first attempt and never actually trying it again.

Regardless, I now have a working configuration, so I can experiment with one setting at a time to find out what I actually need and what makes it fail again. Many thanks, Ignacio.