The fact each part works and the fault is only present when you have both running together suggests to me this is a flow rated fault, I appreciate you have already tested this, however this is the most likely fault, as demand increases if the flow rate cant keep up you will get the fault your experiencing.
I take it you have had the range fully serviced prior to the parts noted in your question replaced (new filter, pump pressure checked, strainer flushed, pressure regulator calibrated and the system bled), since I think this is the area to focus on.
With the fault being constant it should be reasonably straight forward to fault find, for example if the solenoid is being activated to close the flow then you know its a input into the PCB causing the fault, if the solenoid remains open after the cook snuffs out you know its the lack of oil.
It could potentially be the nozzles, but they like other parts should be inspected and you would see a build up of debris which would warrant a replacement, its not like a car where every 20K miles you change the oil or spark plugs, you look at the usage of the oven and change parts which show signs of age.
I would look to try and find out what is restricting the flow rate to the oven, it may just be the oven has a higher demand than the boiler and hence drops out first, the best course of action in my mind is to get the engineer back check the inputs and outputs to the PCB when you start the oven when the boiler is running, then once you know what is triggering the fault you have halfed the problem and can then focus on why the sensor is cutting off the oil, or why the pressure is dropping.
Things like solenoids and photo cells can all be electronically tested, so not sure why they would be replaced if they were not given the desired output, which makes me think this fault could actualy be the PCB itself which despite getting a valid input from the sensors is cutting off the oven. However in any case the engineer who has replaced the part should have check that the fault was still present, have you considered using another engineer to investigate this fault, as it doesnt ring true to have someone come out and swap out parts until nothing is left.
As you have correctly identified the PCB is the control box, it may be a lose terminal, but if it were I dont understand why the oven runs by itself, hence why when the two are running together makes me think the fault is pressure\flow rate related.
I think its worth having a frank discussion with the engineer who has been paid £3K to date, without diagnosing the fault, I would try and find out how he has proven each component at fault before replacing it, as in essence you dont just swap parts out you can test them, eg you can check the solenoid has continuity on the terminals and also watch it activate when you apply a current through it.
The service manual here, shows every component and the structure of your range, as you can see you have already replaced most items, I would be inclined to strip the entire range down and rebuild it, as with having so many parts changed is easy for something to be miss aligned, not connected properly.
On re-reading the service manual there are a host of other items such as the oven thermostat, but clearly if this was faulty the oven wouldnt run by itself, but thats not to say the heat from the boiler isnt triggering it, so again this can be tested using a multi meter, and verify its in the correct location.
I would also draw the engineers attention to the fault finding guide on page 35, that is rather modular and the type of steps they should be testing, then proving the fault by mechanically or electrically bypassing the component. The circuit diagrams for the PCB are straight forward so it may be worth asking the engineer to remove the PCB and reinstall it as per the wiring diagram, and then check all the inputs and outputs when the oven fails to light to pin point the fault.
In summary it sounds like the majority of the parts replaced were not required, and have been changed without any diagnostics, this type of fault will only be found and resolved by testing the appliance as the fault is induced, the components which I would naturally expect to cause the fault have already been serviced or replaced, and the fact the oven starts up and runs without the boiler I feel shows this has to be a oil regulation\flow related fault, and would be inclined to check pressure going to the oven, against the pressure going to the oven when the boiler is running, from here I would then be looking at the PCB to understand if the fault is mechanical or if the PCB is getting an input to tell it to snuff out the oven. Finally by changing so many parts there is a risk the original fault has been fixed, but a new fault has been induced by using second hand parts or damaging other elements eg terminals or wires when replacing the parts, so you cant assume as the item has been replaced it doenst need to be checked both mechanicaly and electrically.
Sorry for the delay in responding, there isnt much in it between the two manuals.
The correct on for your model is here.
With regard to finding the fault, the steps suggested earlier still stand regardless.
Please let me know if you have any follow up questions.
No problem, please let me know if I can be of any further assistance.