Tim, what if you got rid of the offset altogether and went with a straight gimbal (or the old spindle head)? As you flew faster, the rotor "blowback" would increase the inclination of the rotor thrust line. This would amount to a sort of pseudo-stability with respect to airspeed, in that the stick would require forward pressure at ANY airspeed above zero. It would not be UNstable, in that it would always try to return to a certain status quo, but the "status quo" in this case would be a vertical descent.
The OFFSET gimbal head (without spring) does a couple things to alter the picture. First of all, it builds a bias into the flapping/blowback/airspeed relationship. This turns the pseudo-stability w/ respect to airspeed into a more conventional or useful stability. Depending on the offset and the other dimensions of the head, there's an airspeed (now above zero) at which the stick will not be constantly trying to move aft. IOW, the head (with no spring) has a "natural" trimmed airspeed. Above that trimmed airspeed, the flap/blowback principle reasserts itself and creates the same old tendency to return to trimmed airspeed -- which is simply another way of saying you have to hold forward pressure to maintain that higher airpseed. That doesn't seem unstable to me. Instability would mean you had to pull back on the stick to prevent speeding up.
The offset gimbal head also introduces stability w/ respect to angle of attack. Without the offset, at any airspeed above zero, an increase of AOA increases the ever-present tendency of the stick to move aft. This, in turn, tends to increase AOA some more, resulting in a classic case of instability. The offset gimbal employs the increased thrust of the rotor as AOA increases to pull the back of the torque bar up, muting the effect of the jump in AOA. This feature works best if you hold the stick lightly enough for the head forces actually to move the head (floating the stick).
The spring allows us to use extra offset which, combined with the varying spring pull at different airspeeds, increases the airspeed stability already provided by the flap/blowback effect. It seems to me that the spring and the flap/blowback effect work in the same direction -- both contribute to airspeed stability.
The spring also makes the head's trimmed airspeed easily adjustable, without the need to change the actual offset distance.
Finally, the spring becomes a double-edged sword once airframe stability is figured in. If the spring is fixed to the back side of the mast, it is affected by pitching movements of the airframe.* A nose-up pitch relative to the rotor tightens the spring; a nose-down one loosens it. The result is that the spring makes the torque bar and spindle tend to follow the inclination of the airframe. This is a very good thing if the airframe is stable with respect to AOA and airspeed. It's a very bad thing if the airframe is unstable; in a severe case, this linkage could entirely un-do the good work of the gimbal head.
*This is one reason why the mantra "fly the rotor, not the airframe" can keep a student from realizing that a given gyro is simply unstable.