While I cannot tell you exactly what will work for you, I doubt that you will get any attention from Apple short of lugging a 27" iMac to a local store and complaining to them..
But I can tell you what I have done that worked. You can also see what worked for others by reading the thread since I started it last year.
In a nutshell, It's my opinion that it's an audio driver that was introduced with 10.9 in the FaceTime bundle. At least that's when it came apart for me. You will find above discussion about this change.. This is just my speculation as the version numbers of the software matched to others that had the same problem.
I tried a few developer updates in hopes that the Mothership would address this issue and they did, "slightly", but it was still there. And very annoying.
The last thing I tried was clearing out as much garbage as possible. Mail, trashes, log files, etc.. to keep the restore time to a minimum. Then I backed up the entire system and tested the backup to make sure it was intact.
Once convinced that I had a intact backup, I copied that to a different backup drive just in case. From there, I went to the App Store and downloaded the latest Mavericks installer (It should be free). I didn't install it from the App Store, but just downloaded it. From there, I moved it to a 8Gb USB stick and made it bootable. Since your computer came with Mavericks installed, you have to do it a little differently. Please follow this guide and with a USB drive you should be able to achieve the same effect.
http://www.macworld.com/article/2151706/create-a-bootable-mavericks-install-driv e-for-newer-macs.html
(Follow this guide to a "T")
Then I booted from the USB drive, formatted the entire hard drive HFS+ and installed the latest Mavericks version that I just downloaded.
After completion, I set up the system MANUALLY as I wanted it and then tested the Face Time connection and it worked perfectly. After this was working correctly, I did a Migration of selective items.. I only migrated programs that I wanted back, mail items and a couple of other things.. Left everything else. If you do a Time Machine restore, somehow the bad audio drivers make their way back in.. (I mistakenly did this once, and then tried a few more times to see exactly what was doing it to no avail and got bored.)..
Ever since, it's been working great.. I can Face Time with someone and get up and walk around, and the person on the other end can hear perfectly.
Like it used to, and like it should be..
Hope this helps and good luck..