Question about adjusting the balance

I'll start out making my question to the point:

which would be better to use to adjust the balance using a sound level meter, a 315 HZ tone or a "uncorrelated (stereo) pink noise 20 Hz to 20 kHz" test tone?

Now I will add the confusion:  I placed my meter about where my head is when I am listening and checked it with the 315 Hz tone and it was WAY off.  So I adjusted by turning the input level knob (Cary SLP05) way down on the strong side.  Then I measured with the 20 Hz to 20 kHz tone and to get an even reading on both sides I had to turn the side I had adjusted way down back quite a ways back up.

Which do I trust if I don't trust my ears?

That is the uncomplicated the version of the question.  To post the full story, the 315 Hz test tone came from a CD that said to use it with an AC voltmeter to test the AC volts at the terminals (I used the speaker terminals) and one side was about 0.2 VAC stronger (if I remember correctly) so I adjusted the strong side down.  (Also I will note that I checked and the voltage imbalance follows the balanced input 6sn7  tubes, and I do actually have tubes that check dead nuts even, but I was playing with some different pairs.)  So no biggy, right?  Now I have the input knob for the strong side turned a bit lower and I put a small piece of making tape by the knob and made a dot with a sharpy so I could remember where I set it in case I moved it.)

BUT:  now I get the idea to test it with the sound level meter, so I position the the meter where my head would be and use the 315 Hz test tone and now the strong side reads EVEN STRONGER!  I am not trusting my ears so I continue to adust the strong side knob down 'til it is pretty far down but both sides read about even on the sound level meter.  BUT then I find a test CD with the "uncorrelated (stereo) pink noise 20 Hz to 20 kHz" test tone and the strong side is NOT nearly as strong!  So I adjust it to get it as close to even as I can using the "uncorrelated (stereo) pink noise 20 Hz to 20 kHz" test tone

and

it turns out it is about BACK WHERE I HAD IT  after I adjusted it using my AC vm at the speaker terminals.

I guess I should add that this is a VERY nearfield environment with my tweeters, and ears (so therefore my sound level meter) making a pretty much eqilateral triangle of 50 some inches and it is a "dirty" untreated room which I can definitely see having a bad effect on the balance on the sound level meter after I had adjusted it using the AC vm, but why would I get  db readings that were inconsistent (balance wise) with the different tones?  I mean if the balance was off--fine, I can understand that and adjust for it on the meter, but I guess my question is why does it show way far off with one tone and not as far off with the other tone--if that question makes sense.

Thanks.