P. Dirac's string trick does not and may not demonstrate the properties of spin 1/2 of SU(2), as a matter of fact. First, SU(2) transformations are not real rotations, but recalculation rules from one still reference frame to another one. Second, his trick works for real rotations whereas a rotation to $2\pi$ in SU(2) does not change physical (observable) results of spin 1/2 in QM. I heard that he demonstrated his "analogy" for fun, but, probably, he reconned it as an "analogy" rather than as a "proof". There is nothing about it in his list of publications.