1. This has become a he said - she said and it seems clear that the PNR has been noted with the denial. Thus, not likely worth much effort to pursue.
2. Use the FL webform. Sending letters to individuals just means they forward the letter to customer service where it's scanned into the same database which your complaint will reach instantly if you send in a webform.
3. If you want, try filing a webform complaint with DOT. Focus not on the underlying delay, but on the promise made by FL and its failure to live up to that promise.