Thank you Michael.

Given a 3D point on a 3D surface:
Find u and v which map to that point.
Distance on the isoline_u, of the 3D point, from the u curve start point is a starting u guess.
Distance on the isoline_v of the 3D point, from the v curve start point is a starting v guess.
face.evaluatePoint( uv_Guess, u_from_left, v_from_left ) yields a trial point.
...