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Pneumatic soft everting robotic structures have the potential to facilitate human transfer tasks due to their ability to grow underneath humans without sliding friction and their utility as a flexible sling when deflated. Tubular structures naturally yield circular cross-sections when inflated, whereas a robotic sling must be both thin enough to grow between a human and their resting surface and wide enough to cradle the human. Recent works have achieved flattened cross-sections by including rigid components into the structure, but this reduces conformability to the human. We present a method of mechanically programming the cross-section of soft everting robotic structures using flexible strips that constrain radial expansion between points along the outer membrane. Our method enables simultaneously wide and thin inflated profiles, and maintains the full multi-axis flexibility of traditional slings when deflated. We develop and validate a model relating geometric design specifications to fabrication parameters, and experimentally characterize their effects on growth rate. Finally, we prototype a soft growing robotic sling system and demonstrate its use for assisting a single caregiver in bed-to-chair patient transfer.