DRO scales 4-pin connector identification
I managed to identify the connector after exhaustive searching of various suppliers through all 0.8mm pitch connectors. It is a member of the Hirose MQ172X Series with the 4-pin SMT receptacle being a Hirose part number MQ172X-4PA. After locating the part number it is widely available from Element 14, Digikey, Mouser etc.

Rather than make a custom PCB for a one-off I've ordered a couple of DFN-8 to DIP-12 SMT adapters from Proto Advantage (part number IPC0065) that I'll cut in half to mount the connectors to.