All give the same result, Lucy. I also asked the host for help and got the standard "looks good, should be working, we tweaked our end a tiny bit for you" reply only to end up with example.com//the-new-url. I called back and got the "oops, fixed that, all looks good" response a 2nd time... and I'm back to the results mentioned above.
My visitors don't care, but Googlebot is not following the double 301, yet. Is there ANYTHING else I can try?
edit: I tried various wordpress plugins, all give the same double redirect when dealing with a non-www/index.php situation at the same time.