Can the ancestral sin doctrine (and Paul's epistles) survive without a single breeding pair? The necessity of salvation in Christian doctrine seems to be inextricably linked to the view that the entirety of human nature somehow springs from the gametes (and perhaps education) of a single original breeding pair (Adam and Eve's nature &amp; nurture). From the Catechism of the Catholic Church:


  416 By his sin Adam, as the first man, lost the original holiness and
  justice he had received from God, not only for himself but for all
  human beings.
  
  417 Adam and Eve transmitted to their descendants human nature wounded
  by their own first sin and hence deprived of original holiness and
  justice; this deprivation is called "original sin".
  
  418 As a result of original sin, human nature is weakened in its
  powers, subject to ignorance, suffering and the domination of death,
  and inclined to sin (this inclination is called "concupiscence").


Paul's writings had a large role in the development of this theology:


  Therefore, just as through one person sin entered the world, and
  through sin, death, and thus death came to all, inasmuch as all sinned
  (Romans 5.12)


Modern biology doesn't allow the possibility that there ever was a bottleneck of two (or perhaps even one, given that Eve was cloned from the ribs of Adam) in Homo Sapiens history:


Inference of human population history from individual whole-genome sequences
Population bottleneck
Adam and Eve: the ultimate standoff between science and faith


So can the ancestral sin theology and the foundational Pauline writings stand in the absence of an original breeding pair, or do they become meaningless?

(Since this is not a truth question, but a theological inference question please see the comment to avoid arguing uselessly outside the question)
Preface that this isn't a site for debating what is true, it's merely for learning what s taught/believed within Christianity.  See  How we are different than other sites?

With that in mind, most of your question is off-topic, but I believe that the core concept from your question can be addressed if we phrase it as follows:

Do any Christian groups believe that without a literal Adam, the concept of original sin has no meaning?

I'm going to answer that portion, in the interest of answering the heart of the question, filtering out the portions that are off-topic and/or controversial/disputed within Christian circles.



The short answer is tat yes, some Christians, namely Young-Earth Creationists teach and believe exactly that.  Ken Ham, Kent Hovind and other well-known YEC proponents teach exactly that.

One such example from CCEL


  Is it important:
  
  Well, if there was no first Adam, could there also not be a second
  Adam, our LORD Jesus Christ? For as in Adam all die, even so in Christ
  shall all be made alive...it is written, The first man Adam was made a
  living soul; the last Adam was made a quickening spirit." 1
  Corinthians 15
  
  If death did not come as result of Adam's sin, then why did we need a
  savior to deliver us from death unto life? "Just as sin entered the
  world through one man (Adam), and death through sin, and in this way
  death came to all men, because all sinned"- Romans 5
  
  Was Jesus' real if his geneaology account is not trustworthy? Jesus
  was the son of Joseph, who was the son of ..., the son of Seth, the
  son of Adam (Luke 3) - Can the Word of God be trusted for its specific
  geneaology or is it mythology?


I also posted on the subject at Why do Young-Earth Creationists make such a big deal about the YEC view.

Not all Christians see it thus way, of course.  This represents only one view within Christianity.