I had the same thing happen to me in October, but mine was because I had booked as an FO and was a GM and the skymiles number hadn't been taken out & reinserted. I saw the upgrade was "Available" when doing a dummy search, like the OP. I called SMS and they got me upgraded. I sort of played dumb, "Can you help me with this, I don't understand what's wrong, if I reserved this flight today it says I'd be upgraded." A couple of clicks later and she asked me if I wanted a window or aisle.
In light of your frustrations with SMS, it now appears I was pretty lucky, but my advice would be to keep calling back until you get someone who will help you....