The top video in my test uses HLS streaming (single file). Notice that in firefox when scenes switch, or sometimes when you seek, the picture gets distorted. I'm working with the JWPlayer Support but they're telling me that before they provide any support I need to verify that the files were encoded properly, which according to them is:
1) We suggest the Apple standard of 10 second TS segments here. If this is the case, and you are rendering with this, great!
2) We also suggest to place your keyframes at the beginning of each segment.
It sounds to me me like you want to cover a base that is not required. Progressive download would be just as good if not better for Apple devices if you only have one bitrate, saves the player from checking for other streams ( maybe, I am just guessing)
FWIW if you want to really do adaptive bitrate delivery then I can wholeheartedly suggest Sorenson Squeeze 9 Pro for this task, it does it very well.