When I first started with wraps, I used a Moby (stretchy) and had trouble with the over-the-shoulder carries, and found that back carries that way were no good with the stretchy ... so tied her lower down and around the waist, very similarly. It was very comfortable that way. But the wrap was way too long to do it easily, and I never left the house with it because it didn't feel too secure (and since a wrap is way too big for it, it probably wasn't).
After practicing and getting better with higher back carries have found the higher ones (as in over the shoulder, as in the Tibetan) better for me, so not doing the around-the-waist ones anymore.
There are wrap vendors that sell kanga-length versions of their fabrics, *much* shorter than the wraps. Or so I was told ... have not checked that out myself.