This is cool idea. One problem may be that different versions of Android have different versions of libstagefright and just hot-patching that or dropping a replacement may brick older phones.
Here's a more modest idea: Google should immediately issue update for Hangouts and Messenger app that at least disables automatic MMS retrieval. Many users have automatic updates for those apps turned on or maybe at least they'll see a notification about app needing approval to update.
The exploit author told a Forbes reporter that Fennec (Android version of Firefox) has already been patched. If that's correct, that seems to imply two things: (1) MMS is just one of many vectors and (2) apparently somehow the exploit can be mitigated at the app level.
Here's a more modest idea: Google should immediately issue update for Hangouts and Messenger app that at least disables automatic MMS retrieval. Many users have automatic updates for those apps turned on or maybe at least they'll see a notification about app needing approval to update.