Is the concept of reincarnation contrary to the doctrinal teachings of Orthodox Judaism?

There is a difference of opinion among our greatest rabbis whether there is reincarnation or not. R. Sa’adya Gaon, R. Yosef Albo, and R. Chasdai Kreskas for example, believe that after life, one goes to the World to Come where his soul enjoys those spiritual pleasures until, if he merits, he reawakens in the Revival of the Dead. They believe there is no reincarnation coming back to this world, as we know it. In contrast, although not mentioned in the Talmud, many of our greatest mainstream rabbis, including the Ramban, R. B’chaye, R. Yizchak Abravanel, and the Zohar explicitly speak of reincarnation, where one may be given the choice to return to this world to “try again”, and improve himself and his free will, rather than undergoing the difficult intensive educational punishment of hell (gehinom) for 12 months. They see this as an occasional answer to the age-old question of why bad things sometimes happen to good people. Like a child compared to an adult, man, compared to G-d, clearly doesn’t see the entire picture of what happened before (maybe in a previous life), nor after (in the World to Come), and accordingly often can’t see the justice or benefit derived from a certain occurrence or life, which is now hidden from him. Sometimes he may even request a little assistance, to return with a certain limitation or handicap which may have prevented him, in a previous life/lives, from improving a particular given field (such as speech, not to slander, etc.). That being said, everyone agrees with the Rambam that it's much more important to focus on improving ourselves in this world rather than thinking about future worlds or future lives.