Combating flutter with mass distribution?
Do I understand correctly that with this approach, the wing will act similarly to the following model, where the motion is rather chaotic?

No, your combination of masses and springs will have several eigenfrequencies. For aeroelastic analysis only the lowest eigenfrequency counts because this will couple with aerodynamic frequencies at the lowest flight speed. Once you fly faster, the next eigenfrequnecy in line will resonate, but that is only hypothetical because flutter caused by the lowest frequency has already destroyed the airframe.
In very rare cases the lowest eigenfrequency will already couple with aerodynamic oscillations at speeds below stall speed. Then the aircraft can be operated in the gap between the lowest and the second-lowest eigenfrequency.

This should have no certain frequency. Does this mean flutter is avoided?

No, since it has several eigenfrequencies, flutter is as certain as before.

Does this mean flutter can be avoided by redistributing mass around the wing, without increasing stiffness or reducing mass?

Flutter cannot be avoided, only its speed shifted up by damping. The rule always is to place the center of gravity ahead of the axis of rotation (that would be the elastic axis in case of wing torsion), so any movement causes an inertial damping force. This is the reason for the forward location of wing mounted engines.