Hi, I had the same story blaming valve lash adjusters, timing components, etc. there was simple solution. When I changed engine oil I put FIAMM oil filter. That is rubbish. It does not allow sufficient amount of oil to be pumped so you have rattle one second after start up and this annoying ticking sound (Just like diesel engine). so I decided to change oil with the following additions:
1. I put a 1 liter of special liquid for engine flushing to the oil and let it run for about 15 minutes at about 1500 rpm (accelerating from time to time). this liquid also cleans a carbon deposits from the valves and adjusters.
2. There was a tremendous smoke around my car but finally it stops. so I turned off the engine, drained oil (be carefull -extremely hot !!!) and put new oil filter (this time original - Motorcraft). I put 4,5 liters of 5w30 synthetic oil and after 2 minutes engine runs like new - no rattling, no ticking. at least for now.
regards
archie