drift and trimAs you have experienced, the Hawk is a very stable heli that can hover hands-off. It is always a good practice (with any heli after a repair) to set it up as good as possible, just as you are attempting to do....good show.
You can use both TX trim or Subtrim. Using Subtrim is better because then your trim lever can always be checked before every flight to insure they are in the middle. Then you will be sure the trim is the same for every flight. But that being said. Don't forget the primary trim adjustments - the CONTROL RODS. If you get used to always using them as the primary trim and the TX trim functions to "tweak the difference" you will find all will work more symmetrically. I will always trim mechanically until the TX trims require less then 10 trim units.
Tail Drift - Over the 15 plus years I have flown helicopters, I have owned and operated a number of Yaw Rate "piezo" gyros (JR, Futaba, GWS, Century, Arcamax), and I have always been able to trim all of them, even the cheapies, to fly hands off without drift. If you have your throttle/pitch curves set for a relatively constant speed, your tail rotor mechanical control system set for smooth and bind free operation, the revo mixing set properly and your gain set high enough they will all be cabable of this. Ditto for the HH systems.
The key to your statement, is "as speed increases". (I am asuming you mean rotor speed/tail rotor speed). As these speeds change the amount of torque compensation needed changes, so different trims will be required, if you leave all else the same. This is why it is so important with a yaw rate gyro to insure that you have a properly set up throttle / pitch curve, one that keeps the rotor speed fairly constant. On a well tuned system, even the relatively inexpensive gyros can hold through moderate speed changes, as long as the gain is high enough, without the tail wagging.
You might find the article on gyros in the hints and tips section of http://www.leisuretech.ca
of assistance in understanding gyros (YR or HH) and their set-up.