Finally I have some data to add:
Backing date: 2017-10-20
Shipping questionnaire: Never received (possible e-mail configuration issues)
Shipping e-mail: 2022-03-22
Arrival date: 2022-03-29
It took several interventions by @joao.azevedo and others within Purism to get the shipping process underway. Like @stak I ordered an additional battery. DHL initially put the shipment on hold as dangerous goods, even though Purism is authorized to ship loose batteries, but they released it the following day. (DHL told me that Purism hadn’t sent them the paperwork for the battery, but I have had so much trouble with DHL lately that I’m quite prepared to believe that the problem was with them, not Purism.) The shipment left Los Angeles, went via Cincinnati, and literally 15 minutes ago departed from Leipzig, Germany, hopefully on its final hop to my nearest DHL hub in the UK.
Hopefully this will give some hope to people who backed/ordered around the same time as me.
UPDATE 2022-03-29: I have just had a notification that the package has been delivered! 
I’ll pick it up tomorrow, and hopefully I will have time at the weekend to play with it.