Incidentally, the Lohmiller-Slotine formulation may suffer from the same objection that Nelson's stochastic quantum mechanics does. This was articulated by Kenneth Wallstrom. They rely on what's called a Madelung formulation to go between the wavefunction and Hamilton-Jacobi equations + a continuity equation. The HJ equations, however, generate too many solutions unless you impose an additional condition by hand. They have to add something to their theory to deal with that issue.