From a Big Mind view, the idea of reincarnation looses its attraction - and we find a much simpler view.
First, where is this "self" that is reincarnated? The universe is a holarchy - systems within systems from the largest whole down to the smallest energy particle/wave. There are no absolute boundaries - just one seamless fluid whole within which we can discern, but that does not make up any boundaries. There is no fixed or separate "self" to be found anywhere.
Then we see that the world of phenomena is God manifesting, completely and perfectly, in the present. Everything is God expressing, manifesting and exploring itself - a galaxy, the oceans, a river, an amoeba, a human being, a forest, a city, a rock, a car, a cloud passing through the sky, a thought passing through, confusion and clarity, delusion and awakening, Gandhi and Hitler - all are God manifesting completely and perfectly.
So there is only the one whole - beyond all dualities - manifesting. It is reborn - as something else - every moment. Always new, always different, always fresh.
This is the real reincarnation.
And it is far beyond the reincarnation of any imaginary separate "self". At most, it may be that the habitual patterns formed and expressed in a small self continues in another small self, but this is secondary to the real and amazing reincarnation every moment of God - in the present - as the dots on this screen and the awareness in which these dots arise.