From what I've seen the pump might be fine you can get a siphon jet(burner orifice) that integrates compressed air to get the oil to the required pressure.the yellow arrow is the pump thats on it. I was going to replace it with a larger, higher pressure fuel pump form a car with a pressure regulator to make it adjustable. supposedly nothing was wrong with it, but i have not had time to play with it yet. it was cheap enough i bought it on the assumption that it might be toast.
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The thing that seems like a bit of work is the oil heater which also needs the compressed air line to be sunk in the oil via coil so the temperature of air and oil are relatively similar.
Did you take a look at the pdf I sent seems the riello heavy oil burners have the heater and everything needed included though you would have to decide if $500 is worth it compared to the time you would spend diy`ing one, there also seems to be stockist there in Japan.