Can spin and macroscopic angular momentum convert to each other?

First of all yes, you can convert angular momentum to spin orientations, as only the total angular momentum $\vec J=\vec L+\vec S$ is conserved. The setup you describe is very similar to a famous experimental effect dubbed the "Einstein-de-Haas" effect. You can read more about it on Wikipedia. The main idea is that you have a ferromagnet hung on a string and when you magnetize it (which really only means that you orient the spins of the electrons in a coordinated way) the magnet has to pick up angular (mechanical) momentum, since angular momentum is conserved. What you observe is that it starts to turn seemingly out of nothing once you magnetize it.

Now the part where you are mistaken is that you cannot change the spins of particles. The spin of a particle is a property of the particle itself (much like its mass. In fact those are the two properties particles have as a result of their being representations of the symmetry group of spacetime, c.f. Wigner's classification). You can only orient a component of the spin, but not the total spin magnitude. A Spin 1/2 particle (fermion) will always stay a fermion.