Yes Kingwa told me that my Master-6 would be better than the more powerful Precision 2 with the HE6's due to being balanced and simply a superior amp, regardless of the extra power of the Precision 2 never mind the less powerful Precision 1.
So I am not surprised by your experience.
Maybe the Precision 2 would get you closer to the Taurus performance and still be much cheaper?
I spent some hours yesterday comparing my Taurus Mk2 with GD Audio Precision 1 (loaner) and the Taurus was better despite the higher power output of the Precision one. One the Precision one I used the He-adapter and the headphone jack, and tried both low and high gain but compared to the Taurus in balanced mode it was some what thinner in sound quality. The precision 1 is much more powerful giving 22w into 25 ohm and if I remember correctly 7w into 100 ohm but it is only single ended. The Taurus can be tested with 4 pin xlr between single ended and balanced by pushing a button and sounds best in balanced mode on my He 6 and Lcd 2.2. The Taurus puts out 4500mw into low impedance which is much less than 22w but I guess the construction also plays a part. The Taurus costs more than twice as much here in Norway as the Precision one so the comparison isn`t quite fair. Having tried my He 6 with He-adapter from my Line Magnetic 216 IA tube amp and from the Precision 1 without any of them besting my Taurus, I guess its time to let the upgrade itch rest for while and just enjoy my equipment. Try to remember that individual taste is different and you have to commit to your own preferences. Happy listening.