A quick status update:
Due to a mess with transferring payment to the printer (international money transfers... don't ask), my payment was in limbo for some three weeks while I kept phoning banks and things to try and work it out. But the printer has now received my down payment and has begun the process of printing the books.
I don't know exactly how long this takes, but I expect they'll be shipped to Make That Thing by the end of June. And then Make That Thing can start shipping to backers.
Sorry for all these little delays that have built into one biggish delay, but not long now!