Brian, I'd put it the other way. Heavy rotors help keep the nose up when the rotor disk AOA is reduced.
Heavy blades can eliminate HTL, simply by their dead weight. The CG moves up because of all that mass at the top of the mast -- maybe enough to hit the prop thrustline and create CLT. For example, adding McCutchen blades to a Gyrobee should make a CLT gyro out of it.
HTL with no HS requires that the rotor thrustline (RTV) stay ahead of the CG, to hold the nose up. When you flatten out the disk AOA, the RTV becomes more nearly vertical. That requires that the frame drop its nose enough so that the CG swings aft of (the new location of) the RTV. In a gyro rigged to Bensen hang specs, this can result in some hair-raisingly nose-low flight stances -- all because the CG MUST end up aft the RTV for the craft not flip forward from prop thrust.
My 1986 vintage, low-rider Air Command could do well over 80 mph on only 40 hp. Your feet and pedals were so low, however, that the sensation was like sitting in a wheelbarrow that was being dumped. LTL gyros and gyros with adequate H-stabs don't do this big nose-drop when you speed them up.
They also don't become "twitchy" on the controls, which that old lowrider also did.