“Are you saying that everyone reaches the finish line, that every Jewish soul ultimately redeems itself?”
Yes. We have been promised Kol Yisrael yesh lahem chelek lolam haba. As for individual reincarnations and thus bodies, reason why we have incarnations is because each soul needs to fulfill all 613 commandments (except for the kings mitzvos which he performs on behalf of the nation) and thereby refine its portion in the world (divided among all Jewish souls) its soul powers and body parts (which also amount to 613.)
When this isn’t finished, the soul reincarnates into another body to continue the process. The refined aspects of the soul remain with the body that it refined them in, and that body is reincarnated with that part of the soul.
Don’t worry about remaining with an incomplete soul as all Jews are in truth one large soul (that Adam and Yaakov possessed) and any part contains all the rest ( as reflected in the body- which is a proper vessel to the soul- where every cell contains the entire dna – my note).
(See shaarei Geula yemos hamoshiach, page Reish ches tzaddik, for additional information (also fns 15 and 16) the relevant sources in shaar gagilgulim, the Zohar etc.)