Good news on my issues with the Moto Z battery and bluetooth issues! Motorola support sent me a Z2 Play and Wireless styleshell as a replacement for my Moto Z. The additional surprise was that while they were being shipped from China the Moto Z reappeared, repaired with a new motherboard, and returned to me with the remainder of its warranty intact, under a new IMEI. It's got a new battery (previous repair) and is working without any functional issues so far, but has a couple of telltale signs of having been opened up a few times.
So I now have a choice of two phones and a useful wireless adapter moto mod. I also have a spare black nylon herringbone styleshell (if anyone in the UK wants to swap for a different colour let me know). The UK support team in Scotland were very helpful, but it took their intervention and escalation to make progress. I had been using a capable and cheap BQ Aquaris phone since September until this all got sorted, but it's good to be back with a faster and better phone again! I really admire the Motorola Z phones, and hope they can get their support service to a higher level for all customers.