Heh, i knew you were gonna bring that up.
Yes there is progress/regress with each life, but upon the verge of reincarnation is a clean slate. Plus in a linear sense, you really cannot 'regress.' In all this, even the Gods/Time itself die and revive themselves as well as the world, albeit in different timescales. What you did in a past life has no bearing to the choices you make in this one, besides the 'level' of life you exist in. The choice of free will is what defines the soul in Hinduism. Yes, hinduism has its classifications [or caste-ifications if you really wanna get specific] but it's that stratification of society that caused the Gurus/Sannyasins [aka the truly Enlightened] to repel from the structured rule that developed on what they considered false pretenses. Even after achieving nirvana/moksha, a soul can choose to remain in physical form to help others, in Buddhism they are known as Bodhisattvas. History and Indian religions are deeply connected to each other, you can't truly understand one without the other, as they are considered non-revealed religions. I personally believe in a more helical [corkscrew/3D] structure, in that history/humanity repeats itself, but not quite in the same way. Much like DNA, it can mutate.
Jainism is pretty close to Taoism [imo] in that both have an extreme reverence in nature/life, in a kind of 'do nothing, just exist' philosophy. Jains believe Karma is 'krud' on the soul, the desire/intention to be good or bad is what hinders us from the Ultimate Reality.
Taoism however foucses on Immortality, whereas obviously Jains/Hindus believe in reincarnation.