Would it be possible to dry the plane out? Stick it in a warm, not hot, oven
for a few hours? I am thinking that drying it might shrink the screw enough to
begin to loosen it.
Another idea: soak it with denatured alcohol in case some shellac-type finish
has dried in the threads. The alcohol should dry up and not harm the wood. I
suppose the same idea could be done with lacquer thinner for different solvents.
Of course, this method would likely cause the existing finish to have problems,
if that is a consideration.