OK, so when I dug deeper on the phone to Asia Miles, they had recorded my given name as surname and vice versa. I realise that's the standard order in Asia but given they specifically say "name in English" that seems pretty poor.
They corrected it, but required me to send a passport scan. This also seems pretty rich given they screwed it up in the first place and I wasn't looking to change the name.
After that, an Amex transfer went through in a couple of days.