If he says he has flushed the system properly then he has.
But if a system were flushed "properly" there would be no point doing it a further two times, unless by radically different method.
Your faith in your local advisors is admirable, though it took oilski and gasgeezer to prove them wrong about the simple matter of which side of the heat exchanger was involved.
It would be interesting to know what chemical was used in the powerflushing, what procedure was used and how long it took.
However, this WAS a new system so it would be unusual to have all the problems you have.
If you
1) get the water analysed (£25) you will know if something unusual is dissolved and still causing problems
2) put a filter and/or magnetic cleaner on the heating return pipe, you can avoid blocking the boiler and monitor the situation.
You have to recognise that you do not now have a "brand new system". You might be surprised to see how "used" they look after just a few weeks' running with some acid soldering flux left in the system.
It's always possible, as mentioned before, that your radiators for some reason were not as clean as usual at installation. I have tipped rust out of a new radiator.
It is probable that the circulating debris has worn the pump, and of course a pump can always be faulty.