After seeing more photos, I have to agree with the "not quite there" comment.
It seems to me the TASK doesn't really have a niche to fit. Except perhaps a "clean" and smooth confined space (if there is such a thing), or maybe a water rescue? The funnel effect and potential abrasion points on the bottom make it not so practical in the cave environment, and in open vertical drops why would you use a flexible litter rather than a standard rigid one? The latter is easier to handle/position, and easier to rig to. It's just a little larger/bulkier to handle when it's empty.
I wonder if there's a shoulder board and/or some similar form of lateral rigidity in there? I imagine there is, otherwise the patient would have a very uncomfortable experience. Even so, you'd still need an OSS or spine board if the patient required spinal stabilization.
But hey, experimentation is good.
Otherwise we wouldn't have a SKED or any other weird and wonderful contraptions. Many years ago, Aspiring Enterprises in New Zealand came up with something similar (which pre-dates the Petzl Nest). This was the "Rescue-wrap" which is unfortunately no longer produced. Haven't used one personally, but here's a couple of photos that Google pulled up.
(Source
NSW Cave Rescue Squad)
Since I'm off-topic anyway
I thought I'd mention that some cave rescue folks north of the border (ie British Columbia, Canada) have a dislike for flexible litters like SKEDs. They tend to prefer the
Cascade 200 lightweight 2-piece rigid litter, which they swear will go anywhere a SKED will. It's a nice smooth ride for both patient and rescuers, if you can afford the price tag (almost double a SKED or rigid Ferno Washington).