Hi Traveler,
I am familiar with most of the arguments and authorities quoted in your preceding posts, which were certainly exhaustive. I have no intention of re-arguing most of them, as the Church has had almost two millennia to think up counter-arguments on most of the pro-reincarnation scripture passages usually cited, such as those related to John and Elijah, and you are probably familiar with the usual arguments in both directions. The established church and its scholars are entitled to their arguments (which are used to bolster their favored opinions). And, I actually agree with some of them. However, the fact that an anti-reincarnation argument/opinion can be given in terms of a particular scripture does not necessarily nullify pro-reincarnation arguments/opinions based on the same scripture
anymore than the reverse is true. Each must review scripture, weigh the opposing opinions/arguments and decide for themselves. The truth of the matter is that the scriptural witness is ambiguous and even (some would argue) conflicting
on many matters. It took centuries of conflict to hammer out the doctrine of the Trinity, and more centuries to quash all opposition and eliminate Arianism and other counter-interpretations. The ones destroyed and suppressed were seldom evil people, and often not only very good, but very wise and even exemplary followers of Christ. Many good Christians have been punished or destroyed over the years merely for holding opinions opposed to those of the Emperor and/or Church during a particular time period. (Galileo comes to mind). The same was true for reincarnation, though it was mostly held in the earliest eras (as far as I can tell), primarily by the followers of Origen (though probably not by Origen himself). The Empire sought unity, certainty and enforceability and favored certain results and possibilities over others. This approach was taken up by both the Western and Eastern Church, and resulted in some opinions and arguments receiving the stamp of approval and others being quashed as heresy, with their adherents often being punished and eliminated using the cruelest and most brutal means imaginable. The Cathars, as you point out, were one of the victims of this established pattern.
What you seem to be seeking is irrefutable proof based on scripture, where no counter-arguments can be made, and hopefully traditional authorities can be cited in support. I have done the same. As I found, and as you already know from your own research on the matter, you are not going to find this. However, at some point I realized that a search of this type ignores the fact that Scripture is extremely ambiguous about many matters that we seek to understand thoroughly, and therefore allows for numerous possible interpretations. One may take the Book of Revelations as an example. It is a scriptural resource that has been subjected to (and lends itself to) an incredible variety of interpretations over the centuries and continues to be disputed. The same is also true of the first few chapters of Genesis. Hence, the meaning of both of these sections of Scripture have been and continue to be subject to a great deal of argument and conflicting interpretations.
What I have sought to do, perhaps guided by my own background as a lawyer, is to seek out the weak points in the other side's arguments and paradigm as it relates to reincarnation. This is not only because these offer the most possibilities, but because I do not necessarily disagree with the standard Christian positions on a variety of matters. Likewise, I see no benefit in trying to tear down the entire edifice of Christian doctrine when only one area is in need of revision/repair. In terms of the overall paradigm, as exemplified in the two creeds cited and discussed, it is clear that the nature of the intermediate state was not a core concern of the early Church, and does not seem to have been a core concern of the New Testament authors, who seem to have expected an almost immediate parousia and Final Judgment. This lack of attention is mirrored in the eschatological doctrinal statements of the Nicene and Apostles Creeds, which largely ignore the subject. However, theology as well as nature abhors a vacuum, especially when it comes to what was to become an important issue to both Empire and Church as institutions. Predictably, this gap was filled in a manner that encouraged fearful adherence to the edicts of both Church and State: a stunning and horrible threat of everlasting torture in the intermediate state for the disobedient that would be confirmed at the Final Judgment.
In terms of a weak point in the currently prevailing paradigms vis-a-vis reincarnation, I have noted a clear weak point and gap in the only truly ecumenical creed (the Nicene), and a somewhat similar gap in the Apostles Creed. This is as far as I find it necessary to proceed at this point. In terms of the arguments used to support the current paradigm, one glaring weak point is to be found in the bad translation of the original languages. For example, the term "olam" in the Hebrew Old Testament and the equivalent term "aion" used in the Greek New Testament. Neither word inevitably means "forever" or "eternal" as they are used in Bible translations, and thereby used to support the idea of infinite punishment for finite offenses. Both olam and aion stand for what is, at least subjectively if not objectively, a long period of time. Jonah, for example, was said to be in the belly of the "whale" for an olam (which was actually a few days, but certainly must have seemed like a very long period of time!). There are numerous other examples in scripture if you wish to study this issue. The same is true of aion, and likewise for the variations of both of these words. Yet these terms were transformed into terms that indicated everlastingness by theologians to fulfill their own agendas. When it is realized that this is true, various things become much easier to conceive, such as the fact that Gehenna doesn't necessarily last forever. But if not, what happens to those who have received their punishment but are not suited for Heaven? Consequently, the ambiguities in the original languages leave the possibility for something else to help fill the long gap between an initial birth in the body and the culmination symbolized in the form of the Final Judgment and Resurrection. But the foregoing are merely hints and initial ideas for approaches to the necessary research. I have been looking at the matter for a long period, and I believe you will be doing the same.
In terms of the foregoing issues, the Church Fathers and others who advocated Apocatastasis are allies as are current Christian Universalist scholars. Their research and arguments often effectively dismantle concepts of everlasting punishment scripturally, linguistically, philosophically, and theologically. However, they otherwise generally remain unwilling to depart very far from the usual heaven/hell scenarios for the intermediate state. This position typically requires the introduction of the possibility of after death evangelization and/or repentance. These are not bad solutions IMO, and have significant scriptural support (e.g., I Peter 3:19-20 and I Peter 4:6). However, I believe that reincarnation also presents a viable alternative that the foregoing scholars lack courage or perhaps motivation to explore. On the courage issue I do not blame them, as I do not wish to share my beliefs even with my own family

! This is ironic, as I am the husband, father and now grandfather that raised or encouraged them in their very orthodox viewpoints over the last 40 years, but so it goes. I do not wish to trouble them in their faith, nor do I wish to be attacked by the ones I love or excluded from my church due to my own changed opinions.
Cordially,
S&S
PS--In terms of resources, I usually start with the English language Wikipedia. The Italian version may be just as good, but I have not used it and cannot vouch for it. This does not mean that Wikipedia is absolutely trustworthy. In fact, it is indisputably untrustworthy on any topic that might relate to or contradict the doctrines and political stances of modern liberalism and/or leftist ideologies. However, with this caveat, Wikipedia articles are often very useful. I would check out articles on Olam, Aion, Apocatastasis, Christian Universalism, Gilgul, Kabballah, and the various topics that these researches bring up in further online searches. Likewise, I have found it useful to check online Jewish resources in regard to Jewish beliefs related to Gehenna and the after-life. I have also been collecting online scholarly articles relevant to the subject matter for years, but these are not organized and easily accessible (though I have good intentions of doing so at some point

).
PPS--You have mentioned Karma a few times. Perhaps I did not make it clear, but I do not believe that the doctrine of Karma as held in Eastern religions is compatible with Christianity, nor do I believe it is necessary to belief in reincarnation.