I agree with Steve. I'd add that on trying with Apple's API, you're going to have to do some seriously nasty hacking. AVAssetWriter by default spends a second before spilling its buffer to file. I haven't found a way to change that with settings. The way around that seems to be to force small file writes and file close with the use of multiple AVAssetWriters. But then that introduces lots of overhead. It's not pretty.
Definitely file a new feature request with Apple (if you're an iOS developer). The more of us that do, the more likely they'll add some sort of writer that can write to a buffer and/or to a stream.
One addition I'd make to what Steve said on the x264 GPL issue is that I think you can get a commercial license for that which is better than GPL, but of course costs you money. But that means you could still use it and get pretty OK results, and not have to open up your own app source. Not as good as an augmented Apple API using their hardware codecs, but not bad.