Hello anyare! I think I appreciate your appreciation

I'm not an Android developer/expert, so my ideas/suggestions may be totally useless; it seems unlikely, though, that there's an inherent problem in the OS, or everyone and their brother would be clamoring about this issue, and not just on the Samsung Galaxy S III, since Jelly Bean is used across multiple platforms.
I realize that doesn't solve your problem, though, so maybe we can look at what you have/haven't tried already.
Have you done a Factory Reset, and if you did, were things working fine immediately after? Did you restore any previous SMS/MMS, or did you start fresh?
If you haven't done a Factory Reset that would be the place to start. I'd recommend NOT restoring any MMS (SMS is ok), since I have run across problems doing that.
Sent from my rooted, debloated, deodexed Sinclair ZX-80 running CM -0.001 using Tapatalk 2