I've been trying to get this to work since the day I bought the phone. I was using (and still am on my work phone) an inverted AOSP MMS.apk that I just absolutely dig. I was sad when it didn't work on Touchwiz ROMS.
I dug a bit deeper. I got to where you guys were at, I managed to get it to install on a JB TW ROM but it crashed on MMS, just as you all are experiencing. I dug deeper.
I next tried a logcat to see if I could sniff out the issue. Nothing was glaringly obvious as being the issue. I even went so far as to Pastebin it for a well known dev on here, and he pointed it to it being the Gallery as being the issue. Since it's an AOSP app, it was probably looking for an AOSP Gallery. So I tried that. I replaced the TW Gallery with the AOSP Gallery. Still, nothing. The dev hasn't had time to really help me out since, he's a pretty busy guy and isn't even supporting the device, he was more helping me since we're more friends than anything else.
I'm going to see if I can get ahold of another dev on here and see if he can spare some time to help. Problem is, he doesn't have this phone, but I do believe he has a Galaxy Note, or the Skyrocket. I PM'd a few devs supporting our phone with ROM's to ask if they could help, and I didn't receive a response. If anyone knows anyone who can help, I'd be glad to pass along what I have.
I would REALLY like to get this working on TW ROM's. I'd settle for the old school AOSP inverted one I'm using, but the CM/AOKP one is probably pretty similar.
Current: Samsung Galaxy S4 (SCH-i545)
ROM: MD2 Stock Odexed