You're always welcome, PM me when you want to make it happen someway.
Your discription means it sounds like the usual amplifier white noise. Maybe (or not) more grainy, as what you hear is probably the DAC's residual noise, not the amp's, and DAC's noise usually isn't that "clean".
3-4 bars on iPad is really low level, I just listen to Ryuichi Sakamoto Beauty album on 9 bars (USB2 with Lightning Power Camera Adapter) on my iPadPro 10.5, which is about the level of my own voice when I'm talking. So you probably have a very sensitive hearing.
I just had my hearing tested by a medical audiologist and she told me I would have the hearing of an owl. Maybe she meant a little older owl
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I have all the equipment to measure and analyse the noise if it's somewhat above the threshold of hearing. I have to see which of my Bruel&Kjaer measurement mic's have low enough self noise, but I have several 1" ones and a B&K 4142 artificial ear - and a very quiet room in my recording studio.
So far I didn't think it's necessary as I don't hear any noise, but it won't hurt to do it.
BTW: Studio recording mic's have too high self noise (except some of the latest Neuman ones) to record the noise, as you may find out if you try comparing recordings with Mobius switched on and off - if you hear a difference in the recordings the noise must be really bad.
With my usual 1/2" B&K mic on my 4143 artificial ear I could not detect any noise, the mic's self noise is too high.