Thanks!
Actually, since I wrote that post things have gotten a bit better.
Looks like their useless new system had caused a load of issues for my AME submitting all the data. Sounds like they'd had it for a month, but hadn't done anything with it because "computer says no".
I've now spoken to an assessor who's reviewed my case, but I need to make an appointment to see one of their specialists. Unfortunately, and quite predictably, now their appointment booking system is U/S!