Gravity Failing

When the arrow points to the bottom right, the cage is a Young Tableau, but something’s gone strange in this puzzle, and gravity seems to be pulling every which way. Some cages are upside-down or reversed or both, but the arrow always points in the direction of strongest gravitational attraction.

Rules:
Normal Sudoku rules apply.
Within cages, digits do not repeat, and larger digits are pulled in the direction of the arrow. That is, within each cage, rows increase from either left or right, while columns increase from either top or bottom, both in the direction the arrow is pointing.

Estimated difficulty: 2 out of 5