I have no intuition for this. Maybe it's valid, but your other two examples raise grave doubts about this one.

> Or you throw it at something of known mass and measure the speed it imparts onto the known object.

Blind application of the principle of conservation of momentum does indeed tell us that we can measure the mass of one object by colliding it at known velocity with another object of known mass and measuring the resulting velocities. But I tend to worry that the mechanism for transferring velocity from one object to another object in a collision is the force it exerts during the collision, and that that force might be determined by the object's weight (also a force) rather than mass (a platonic concept). But, I'm not sure here either.

This ties in to the "fun factoid" that physics has no explanation for inertial mass and gravitational mass being the same quantity. If they in fact aren't necessarily the same thing, momentum transfer, measuring inertial mass, would solve this problem. If there is a reason they coincide, this approach will be confounded by that reason.

> Or you hang the a known mass and the unknown mass on strings and measure the force of gravity between them

I'm absolutely certain this wouldn't work to distinguish the mass and weight of an object that has extra weight because it's emitting extra gravity. The measured force of gravity is going to include the extra gravity you're trying to ignore.