Phew. Finally got there and booked all 14 (!) days in September. Interestingly, our UK tickets usually allow us 15 days even though it's a 14 day ticket, so we could go either on the evening we arrived or the morning we check out. Not this time, we got to 14 and that was it - no more reservations allowed.
A tip once you're in, if you're making multiple reservations, DON'T click 'View My Plans' at the end, instead of 'Make Another Reservation'. I did that by mistake once and got booted back out to orbit..
The system was actually very smooth once I was in - pages loaded briskly and it was very clearly and neatly tied to our reservation. Just appears to be bandwidth/volume that was the issue.
You'd think they'd just pay the extra for a few days of extra capacity... But what do I know...