Then the first thing you need to do is to immediately stop using your ears to determine this. An accurate reproduction of the source material can not be determined by listening to test tones to try and determine how neutral the response of a speaker is in your room, nor can your own hearing.
To achieve an actual neutral response in your room, you need measurement software James. REW shows large-ish deviations because those large-ish deviations exist, far worse than you can even imagine by looking at some measurements posted here. Doesn't matter what software or hardware you use.
What I posted has nothing to do with Fletcher Munson.
And this goes back to the very beginning of your questions.... You make wrongful assumptions regarding human hearing. It doesn't appear to me that you are actually open to learning anything and you are set in your ways, which is fine. But I am signing off on this until you actually take the proper steps to learn more. You don't even need to use REW, just read some books on the subject.
In summary, the goal of a neutral speaker is to reproduce the source material neutrally, keeping deviations from neutral linearity to a minimum. Determining the actual accuracy of a loudspeaker can only be done with proper anechoic measurements. Once you place that neutral speaker in a room, where it is subject to room modes and reflections, all bets are off. At that point, how the speaker reacts in your room is characterized by the directivity of the speaker.
To further complicate things, humans do not "hear" neutrally. When you think you hear one of your test tones at the same amplitude as another frequency, you are then taking into account the response of your room, the response of your own hearing and the directivity of the speaker. If you were to actually measure this, what you hear as being neutral, would absolutely not "look" neutral to you but would to many people on this forum due to having experience in this subject.
For example, go online and listen to some white noise. White noise is a flat frequency response, or equal energy for each frequency. It is going to sound thin and bright to you, definitely not neutral to your ears. Now go listen to some pink noise, it will sound far more neutral to you, but is anything but neutral with regard to the frequency response.
With regard to achieving your goal in your room, you already have very neutral speakers. The next step is to deal with your room, and you can't do that without measuring its acoustics. Once you have that information, you can then work on room treatments or add EQ to deal with room issues. Once measurements confirm that you are achieving a decently neutral response, you will need to see an audiologist, have your hearing tested from 20kHz to 20kHz. They will provide with you an estimated frequency response of your own hearing. You can then use the inverse of this to add that as a target curve for your equalization... At that point, you will have achieved your goal.