You shouldn’t have a problem. My point before was about going from 3.5mm unbalanced to 4.4mm balanced… that is, going from 2V to 4V, ~125mW to ~250mW, you may hear the sound quality improve. You will also hear the volume increase, but for the same volume I’m sure I heard the bass get punchier and possibly better dynamic range.
Altho controversial, I’ve heard several reviewers claim this is a real side effect of giving the S12s more power. Personally and in my humble opinion, I believe this is otherwise psychoacoustic and in my head, but I am willing to believe that for amplifiers that provide barely adequate power, and then changing to an amp with more power, the change in sound quality may indeed be real. On the other hand, for going from a more than adequate amp to another amp, it becomes more difficult to assign differences in sound quality to the difference in power. It’s as if, when using barely adequate power, not all frequencies respond the same way (i.e., predictably, relative to volume), but if given an amplifier that provides a lot of headroom, all frequencies behave more predictively.
So, in summary you should be fine with any amplifier, and although many would be considered overkill, you’re not in any danger if you’re careful, pay attention to the volume before plugging in, and always make sure you’re in low gain mode.
Edit: as an aside and example… I’ve recently purchased the Topping DX3 Pro+ small desktop DAC/Amp for my bedside table. It will provide much more power (1800mA into 32ohms) than my IEMs and HPs require, so I was comfortable with the unit not providing a balanced HP output.
Also… I didn’t mean to ignore your “outside vs inside” question. I imagine if your ear tips provide for good isolation it wouldn’t make a difference…