Android message merge with iCloud Message history
For the record, Apple's Move to iOS app does work. In the end, I had to:


Borrow an old Android phone (i.e. pre Android 9).
Transfer the messages to that from my Android phone using SMS Backup and Restore.
Reset the iPhone so the Move Data from Android option was available – only possible when first setting up the phone.
Use Move to iOS app on the old Android phone to copy messages to iPhone.
Sign into iCloud on the iPhone to enable Messages in iCloud, which then merged the newly transferred messages with the ones already present in iCloud – I've confirmed that this has worked as the imported messages have synchronized to other devices.


The Move to iOS actually still wouldn't restore to my iPhone XR, so I had to restore to a borrowed older iPhone, then backup that and restore it on the new iPhone… Apple last updated this app in March 2016, predating the iPhone 7, 8/X, XS/XR generations, so hopefully it will get some attention soon to fix these issues, as not everyone will be able to borrow other devices to go through this process!