Look, headcanon is all and good, but in the original Japanese, they use the exact same word for what happens to the Moon Princess and the rest of the Senshi, IRRC.

Reincarnation just means that you have the same soul (especially in the Sailor Moon verse) - Everything else is optional.

And all the reincarnated version don't have the same personalities as in their past lives in all three canons (Manga, anime, Live action)