I called Toyota Online earlier for an update (as I know I won't be getting one from my nominated dealer...) and to ask when they're intending to take the cash payment, as I was told a couple of weeks ago that I was in the first batch of early December deliveries and was on the list to request the payment some time next week.
This prompted them to send me an email requesting the payment, which I received pretty much right away. Whilst they couldn't provide me with a specific time frame for the delivery, they said it was due to be delivered "soon", which upon further probing meant "within 10 days, maybe even sooner".
Take it with a pinch of salt, there's a lot of reluctance by Toyota Online to give us any definite timescales, and I don't blame them for it (judging by past experience), even though I think it should be them giving us an update, not us chasing for it.
I share my frustration with all of you but please make sure to be polite and professional in any interactions with the customer service staff, as they're almost definitely not the ones to blame for this circus (which I'm sure all of you are anyhow).