you wrote:
What makes it tricky is not knowing what was rotating inside as well as how much mass it had.
But you have additional clues, and you can count them up.
the weights are shaped cylindrical
one weight has about 4 pounds,
the weights act in pairs
you have the diameter of the wheel
you have the rotation speed
you have 8 impacts per turn
you have the material of the outer wheel, wood
all the dimensions of he wheel can be measured from the drawings
you can calculate the mass of the outer wheel
The wheel was started with a finger push and accelerate.
It changes the status from well balanced to overbalanced.
With 8 impacts per turn you can calculate the oscillation frequence.
When you have calculated the mass of the wheel and you like to accelerate this mass, then you need an internal torque.
The mass of the internal weight is 2*4 pounds, or 4*2 pounds...2n*4 pounds.
The distance for a lever is limited to the radius of the outer wheel.
As one weight is going to the rim and the other to the axle,
only one of the 2 weights is responsible for the torque,
then swap.
More weights, more torque.
A greater radius more torque.