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.