Becca - great summary! However, I need to make a couple of corrections:
You can certainly file eAPIS via your iPhone & iPad now. If I may plug my app, please see iAPIS on the App Store. It's a free download and has been fully certified by the CBP after several months of testing with them. We do make a small charge per filed manifest (currently $2.99) but we believe the way the app streamlines and simplifies the eAPIS manifest filing makes this charge worthwhile (Fltplan.com charge $250 for a similar service!).
When returning to the USA you must phone the CBP at the airport of arrival before departing, as well as filing the eAPIS manifest.
Also, it can be a bit confusing knowing what you need to do if some aspect of a flight changes (some passengers are no longer travelling, or date or time of flight is changing). The CBP have rules on this and we have summarised there here:
http://iapis.tenderapp.com/kb/eapis/manifest-changes-do-i-need-to-resubmit-a-new-manifest
If there are any questions on eAPIS or even on the iAPIS app then feel free to ask me.