This is the stock Android 4.1 MMS (and SMS) app backported to ICS, and converted to only use public APIs. Actually the SMS ContentProvider is still private but that is unavoidable.

It's in the Play store - search for "Jellybean SMS".

I don't have time to work on this anymore. I'm mainly uploading it so people can fix the following bugs:

• MMS doesn't work.
• Notifications are very hit-and-miss. Really the only way to fix it properly is to make a private SMS ContentProvider rather than trying to coexist harmoniously with the system one.