As a Christian,
this verse teaches that after we die there is judgement, so no reincarnation.
If you actually study the doctrin of reincarnation, which comes from Hinduism, what you come back as depends on how you live. The ultimate aim is to progress and reach nivana without slipping down. As a consequence of this teaching, there is immence poverty and cruelty where it is taught in India. If someone is destitute and in the gutter then the attitude is that they deserved it because of how they lived in a former life. If you help that person you do them no good, as they will be reincarnated back into that position or worse, so when you see poverty and suffering, walk on by. Do not assist, as they deserved it due to a past life and you do them no good.
I realise you are doing some kind of party game, but you fall into the trap that proponents of "New Age" thinking lay, by watering down what Reincarnation teaches and its implications. Even Ghandi described the doctrin of reincarnation as "a price to great to bear"
That said if I were granted the privilege to live on the Earth once more, it would be as another human male living in good old blighty.