If it was a manual I'd suggest what I had to do with mine when the batteries (24v) went on the fritz... Reverse park on a gentle incline, and hope the cardan shaft brake holds and it's still there when you get back. Of course, every time I did that the batteries were still good when I got back and it was only when you had no option but park on the flat that they would be dead in 5 mins...
Basic checks you report would indicate that the alt is not playing the game, but on these the earthing setup is a common culprit as well as a buggered battery. Swapping the battery out for a known good one and seeing what happens to the warning lights is a start (I'd suspect they would go out) and then rechecking the alt. It's the right time of year for all of these to end up dead though.
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