I find this especially true when moving them close to the ears. Could it be the dished shape?

bluetooth is a digital transmission. The volume is encoded in the signal, it can't get louder just because it receives a clearer signal.

Unless the reduced power consumption by the transceiver causes the battery voltage to rise noticeably.

Empirical evidence says otherwise. Bluetooth headphones on desk, can hardly hear anything. Touching my head (particularly the ears), loud and clear.

Ohh, I need to work on my sarcasm detector.