My last post seems to have got lost.
Nothing in the workshop book that seems to help. Except purge valve opens only when engine is warm. If its opening when cold it will allow excess fuel vapour to be breather and then the O2 sensors may throw a wobbler that could lead to rough running. It does explain why the dealer replaced the temp sensor, MAF cannister and purge valve, I can now see their logic. They reckoned running with purge valve open / part open was enough to mess up the MAP sensor....
Have you first tried fuel system additive / cleaner?
See if cleaning the inlet manifold and throttle body help.
If not my first port of call would now be the temperature sensor.
We had an exhaust leak on our 169 that caused funny running, so I would also check the flexi section of the exhaust and the whole system for loose clamps / leaks.
Being a p

igate spender if all else fails I would do all the sensors mentioned and the cannister as a set as doing part of the job was a very expensive to do on our car as we had a second bout of trouble and as you say the bill was eye watering even without tappets and MOT.