Not all pumps flow the same at the same fuel pressure. Its like comparing a k03 to a rs6 turbo. @ 20lbs of boost the rs6 turbo will have more flow compared to the k03 @ 20lbs. Same idea with the fuel pumps. You will need to tune for the specific fueling setup.
You are a little bit right but your conclusions are completely wrong.
It is true that pump's MAXIMUM flow differs between fuel pumps at a given pressure. "MAXIMUM" is the important word here. The pump always pumps at 100% of its flow at a current fuel rail pressure which is regulated by FPR installed in fuel rail. From there, the injectors dictate how much fuel is injected into cylinders and the rest of fuel is returned back to the fuel tank.
So long the fuel pump can flow enough for a given fuel rail pressure, it doesn't matter how much it actually can flow. If 100 l/h is needed and your pump does just that, 100 l/h or 1000 l/h, the system will not see any less or more fuel injected since the pressure will remain constant.
Now, you said that you tried numerous tunes and have the same problem. Are you injectos the same as the tune is using? The only reason I could think of why you could see much more at part throttle but almost perfect at idle completely incompatible tunes for your injectors' TVUB/KRKTE values. E.g. your injectors flow much more than KRKTE in tune indicates with large enough TVUB to mask this fact at idle... but rearing its ugly head in part throttle where KRKTE weighs much more in calculating fuel mass.