So, finally, my solution to all this.
It turned out that the sticky residue is soluble in diesel, so I got a gallon of white from the local garage and a bulb-pump (they type used with outboards) and pushed it through my fuel lines, including the lift pump and priming pump. Then I ran the engine on the white to draw it though the injector pump too.
The main problem was caused by the sticky residue gluing the inlet valves shut and the spring pressure from the pump insufficient to pull them open. A positive pressure from the other side solved that.
I drained the main fuel tank and washed it out with a 50:50 mix of white diesel and paraffin using a garden spray. Using a temporary tank linked into the fuel and spill lines, I could then drive the boat to our nearest marina to put some red into the tank.
Fingers crossed that I never have to do all this again!