It would proably be best to take this question to a developer forum as this is a customer forum.
However, I would suggest filing a bug using <https://bugreport.apple.com/>. You may log in with your Apple ID. If you need to turn your Apple ID into a developer account, sign up using the free Safari Dev Center. After that, you will be able to log into bugreport.apple.com and file a bug in Apple's internal bug database.
Some things you should include in the bug report:
- Explicit steps to reproduce the bug.
- A stand-alone test case if possible. (Sounds like this requires some server-side software to be set up, so instructions on setting that up are required.)
- A tcpdump of both a failed POST on iOS 7 and a successful post on iOS 6.1.x. (Make sure to pass "-s 0" to get the full body of every TCP packet.)
- Information about workarounds or alternate tests you've tried (like the AJAX/XHR test you mentioned above).