So you just went to an auto supply store, got any old in-line fuel filter, cut the rubber part of the supply line, and just inserted the filter with some hose clamps? Sounds like a 10 minute job. And this won't reduce fuel pressure or bring anything out of spec? Could be an effort well spent.
I am still curious if a bad cold start injector could have anything to do with this. Also, since cleaning the idle air valve does not take buying any parts, that could also be an effort well spent. You said spray it with silicone - do you mean a silicone lubricant, such as silicone door spray?
One thing I noticed is when the engine is cold, the idle speed fluctuates (I described this earlier), then settles down as it heats up. I can clearly hear a "clack-clack-clack" sound coming out of the front of the valve train in cycles - it comes and goes with. This sound continues in cycles even as the idle speed settles. Which is why I suspect a bad chain (It takes 8 revolutions of the chain to go through, so if a bad area of the chain passes It could be throwing the timing off, confusing all that lovely digital technology.) That's why I fear the whole thing may be out of whack.
It has plenty of power, it's only the idle stuff that drives me nuts!
1989 560 SEL (black/black)
2001 Audi TT Roadster (silver/grey)