Lowest Fuel trims achieved only in the 1200-1500 RPM range?

Keep looking for an air leak. I just fixed a lean bank code on my car that would illuminate at some speeds and not others, similar to your situation. It was due to a very slight vacuum leak around the PCV valve and the PCV valve itself. The spray solvent trick did not work for me, since the leak was very tiny and I couldn't discern an rpm drop. The leak was in fact so small I doubt a smoke test would have identified it. I was amazed at how such a small leak -- actually several leaks way smaller than a pinhole -- could cause a code.

I once read that about 80% of vac leaks are related to the PCV system. In my case, the code disappeared for a time if I just jiggled the pcv valve. The air hose that connects the valve was brittle due to age, so it didn't fit tightly. I sprayed the hose with PB B'laster and added a hose clamp to remedy the situation. Dirt had also accumulated inside the rubber grommet into which the PCV valve is fitted. As it turned out, the PCV valve was also the wrong part number, probably installed by a mechanic years ago. While researching my problem, I read further that a loose o-ring on the dipstick and worn crankcase oil filler cap on the valve cover can both upset the vacuum of the PCV system. Some cars have plastic connectors & elbows in the PCV circuit that develop minute cracks from heat stress, so be sure to pressure test them with the car off. Since PCV continuously sucks oily vapors from the crankcase, it is prone to sticky buildup and, as such, benefits from a few shots of carb cleaner through the PCV valve and tubing (with the PCV valve removed) at idle.

Looking back, I missed the whistling sound that the leak was generating. It was mixed with the usual engine sounds at idle, and I had grown accustom to it. Once I became aware of what I was hearing, it was still very difficult to pinpoint the location of the whistling because it seemed to magically change location depending on where I positioned my head under the hood. Some people use a cardboard tube (from a roll of paper towels) over their ear to narrow the acoustics.

As you can see, my code was triggered by a combination of several small problems. No wonder it lingered so long before triggering a code and was so frustrating to fix!