on paper, a B22 should have no problem powering the HE6.
if you go with 2.5" heatsinks in both the O22 and B22, and size the TX appropriately, 200-225mA quiescent current bias should be achievable, or 400-450mA Class A swing. i think there are sonic differences between 160mA and 200mA. depending on preferences, you may like one better than the other. balancing doesn't double the Class A current delivery since the outputs are in series with one another.
assuming a source of 2Vrms, a gain of 5x or 10Vrms v-swing isn't enough for the HE6. to achieve the full 15Vrms the B22 is capable of, you need to go with a gain of 8x. for balanced/4Vrms this means you need a gain of 4x. if you want to swing the full 30Vrms that a balanced B22 is capable of, then a gain of 8x would be appropriate.
just because your pot may be sitting at 3-5 o'clock doesn't mean the amp is "under-powered". it's a function of gain.