Getting the first ball: perform an autopilot. Tap the wedge and quickly lift the lift up.
Getting back to the draggable. Perform boogey bot. Let B stand next to the concrete pillar where the ball has previously rested on, and quickly tap the grass block and the pillar until B falls down into the draggable. If this fails, repeat the process. Also, notice B's feet if they're slightly positioned off-grid, then you could just tap the draggable below.
Time for the 2nd autopilot. Tap the ball and quickly drag the lift downwards. Make sure to position the lift a block lower from the pillar.
Nudge the 2nd ball.
Getting out into the white space. Time for the SSS trick as shown below:
Possible unexpected bot behaviors:
1-B might fall down directly into the fallen object after performing the first autopilot. (Happened to me once out of 54 tests)
2-B could be stuck on his way to the movable resting on the ball. (probability: 3 out of 20)
3-B might push the movable so hard that he might push and ride the ball away from the level. In some case, towards the win. (probability: odds are astronomically low)