The paper focuses on the welding task planning for the robotic station with a till-roll or balance workpiece manipulator (positioning table). In contrast to the previous works, the downhand-position constraint, which requires the weldline to be horizontal and the weld normal vector to be opposite to gravity, is relaxed. But, to ensure the prescribed quality, the downhand deviation is charged by reduction of the welding speed. For such settings, a novel method is proposed for the welding operations planning with the minimum-time objective. It is proved that the corresponding optimization problem may be formulated as a specific case of the generalized traveling salesman problem. For this problem, an efficient heuristic algorithm is developed that produces both the optimal welding cluster sequence and the positioner optimal motions. The algorithm efficiency is verified for a number of random test problems and is also confirmed by an industrial case study