Sorted. It looks like there *was a problem with the website earlier, and then in my irritation I mistyped my e-mail address while creating the second account so the confirmation e-mail was instead sent to firstname.lastname@example.org. Hee! Ooops. So it was partly Amazon's fault and partly my own. So I've logged into the second account. The DVD is listed in it's order history, and the recommendations based on prior purchases is hilarious, it's pretty much just a big list of everything Paul Gross has ever been in.
The DVD is due to ship tomorrow, and should turn up whenever it turns up. Probably some time next spring if Royal Mail carries on the way they are.