I read everything and it's a pretty nice fighting style. I think we could focus on just giving cloth this animalistic transformation, while giving it motion, making the style really separate from the Bandage Arts, which simply give bandage/cloth motion. Both techniques are good supporting techniques, but aren't that good to use on their own. If we bring cloths we won't be able to give them motion with just the elemental infusion, and we need actual teddies to use the second, which isn't something a normal ninja has readily available.
I've thought about some jutsu, here are the ideas:
Description: The user charges chakra through any available cloth ( of his/her own, not the opponent's clothes ), and shoots it out towards the target, as laces of cloth that move at the speed of an arrow. With one handseal, done through the usage of just one hand, the string will twist around itself and turn into a snake made of cloth, which will then wrap itself around the target. The cloth is thick and resistant, and allows the user to utilize the animated snake cloth to bind an opponent or simply swing around for fast travel or evasion. With an initial double-handed handseal, the user can summon laces of cloth from within a scroll/tattoo, with the kanji for "Lace", which appear around one's limbs or torso. The snake has tiny strings of cloth popping out of it's body, making it look like a soft and hairy plushy, though strings can have a more rigid consistency to make them look more like sharp scales.
Description: Allows the user to summon a cloth plushy, or teddy from within a scroll or tattoo seal. The seals for these cloth toys are marked with the kanji for "Toy" and require a one handed handseal to unseal. The cloth teddies are usually the size of a fist, and represent a wide variety of animals, from gorillas to birds, including hybrid and legendary animals. They serve as a quick access of material for the Oversoul user to manipulate. On their own, they are harmless, and some can even say they're very cute.
The user can, otherwise, simply use this technique to summon a blanket of cloth, of varying width and length, instead of an actual cloth toys.
Description: The user throws a piece of cloth in the air, before perform 1 handseal, infusing the cloth with chakra. At that point, the cloth will shred and divide itself into multiple pieces, no more than 10, which will then turn into various small sharp-beaked birds, akin a kunai. They have a long neck and a small wingspan, like weird looking flamingos. After the handseal, the cloth shreds, turns to birds and shoots itself towards a target, in a fast succession. The kunai flamingos can be shot in a converging or a diverging trajectory for focused shots or a more spread out damage output.