Each channel of a balanced amp has two amplifiers in it (so four actual amps for a two channel amp). The output is taken as the difference between the outputs of the two amps in one channel. This is using the balanced output.
However, when you plug into the SE jack, because the headphone wiring is taking the signal from the output to ground, you can only use one of the amps in each channel. This is what I meant by half of each amp. You are only using 1 of the 2 amps in the channel because your phone connector and headphone wiring are forcing you to do that. There can be exceptions to this, such as a transformer output where the grounding is not an issue.
When you use only one of the amps in the channel your maximum output voltage swing is no longer the difference between the two amps, but only the maximum swing that one amp can do. And since this maximum swing is, typically, half of the full balanced excursion, you only get 1/4 the power since power goes up as the square of the voltage.
The amp doesn't really have a mode. That is, with either balanced or SE input (with internal phase splitter) it is always running fully balanced. The only difference is where you take the output from.
If you use the balanced outs with balanced headphones you get the full performance of the amp. If you plug in to the SE TRS output you only use one amp in each channel and, while the output of the full channel stays the same, you are leaving 75% of it on the table, so to speak.
The other advantage to using the balanced output is that the noise will be lower because of what's called common mode rejection of the PS noise.
Let me know if this was useful.
So using the SE output takes the voltage down to about 350mA is what you're saying, but it's still balanced audio. Correct?