Steve, the short answer is that you are not going to be able to get the kind of results you want using AVPlayer. The h.264 video logic included in iOS is really great at playing video and video/audio together, but it really sucks at starting/stopping and switching from one clip to another. The reason is that there is a lot of buffering that needs to happen to load up and start playing a h.264 video in hardware. Basically, you need to roll your own code that sets UIImage/CGImageRef for your views in a way that makes it easy to switch from one clip to another by simply switching from one array of UIImage objects to another. Of course, that is easy to say yet not so easy to implement.
What I would suggest is that you evaluate existing code that already implements this logic instead of rolling your own. For example, have a look at this StreetFighter demo app. It shows how a very simple game like iPhone UI can be constructed using a series of clips that show a character doing a kick, a punch, or throwing a fireball. The results looks like this:
I also wrote up a blog post about seamless-video-looping-on-ios. You can of course roll your own code to do all this, but I would suggest reading more about my library at the linked website as it will save you a lot of time.