It's probably too late, but your email is way too long. All DL needs is the facts, not the long argument. I would simply say:

1. I qualified on Date XX/XX/XXXX with flight YYY from AAA-BBB
2. Did not receive proper full credit for the full segments:
List

Please credit the missing segments. Thank you

When writing to CS, brevity is always a major + and you should only include the facts not the argument.