The talk of reincarnation sounds like believer in the Hindu religion
"Reincarnation: It's Background
Reincarnation comes from the Hindu-Buddhist philosophy of soul transmigration. This is the "religious" concept of the eternal birth-death-birth cycle, where a soul moves from body to body. The status of each successive body, whether human or animal, is the direct result of the quality of the life the soul led in the previous body. Thus, a "good" life results in rebirth to a higher quality form, and a "bad" life results in rebirth to a lower quality form. This forward and backward progression is based on the Law of Karma, a central foundation of Hinduism and other Eastern-based philosophies. As most of us know, Karma teaches that good deeds are rewarded and bad deeds are punished. The ultimate goal in this Karma cycle is for the soul to progress to the highest level of existence and become one with the universe. Reincarnation is taught side-by-side with pantheism, the belief that everything is God and God is in everything. Reincarnation and pantheism are the central doctrines of Hinduism and occultism, variations of which have grown popular in the Western world in recent decades.
Reincarnation - The Truth " (all about spirituallity.org)
If there were true reincarnation, then the population of the world would never grow. How could it if everyone just came back as someone else? Also, if anyone has noticed, those who speak of reincarnation hardly ever recall a past life where they were normal everyday people. The usually claim to be royalty or Napoleon or someone of note. Now everyone can't have lived a past life as a superstar. There are too many of us ordinary people in the world. And that number is growing everyday.
The idea of "cleansing one's karma" by the cycles of reincarnation includes coming back as higher and lower beings. Animals and reptiles and/or humans depending on how clean one's karma was at the time of this death.
Ultimately the goal of reincarnation in the Hindu religion is to cleanse one's karma and to keep moving up on the "wheel of life" until one becomes one with God.
And as to heaven and hell being really crowded, most religions don't believe that you take your body with you and so your soul wouldn't take up all that much space.