Strip lines now stop at a full-length horizontal cut-off that clears the
parts instead of slicing the band beyond it. The desktop dialog and Plan
Cutting also propose their own horizontal separator when that band beats
the X tail (opt-in for API callers via KeepHorizontalRemnant); a kept X
tail beside the band becomes a corner piece whose separator stops there.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>