FINALLY, Success!!
Here's what worked:
I should clarify... I was looking for ANY working settings that would make sending pics via MMS work for a Samsung Galaxy Note 2, unlocked International model GT-N7100, on Straight Talk's AT&T network. I finally found them! Here are the settings that worked for me for sending MMS pictures, when all others failed. I believe these are the same settings posted as a screen shot by ayg. Thanks ayg!
Name: Straight Talk
APN: att.mvno
Proxy: Not set
Port: Not set
User name: Not set
Password: Not set
Server: Not set
MMSC:
http://mmsc.cingular.com
MMS Proxy: proxy.mvno.tracfone.com
MMS Port: 80
MCC: 310
MNC: 410
Authentication type: Not set
APN type: default,supl,mms <== NO SPACES between values
APN Protocol: IPv4
Enable/Disable APN: (checked/APN enabled)
Bearer: Unspecified
Notes:
These are for the International version, model GT-N7100, unlocked. It seems to matter a lot which device you have as to which settings work.
I've tried ALL manner of everyone else's APN settings that the SWEAR work great for them on their phone. NONE worked for me until these.
Anything that involved changing MNC from the default of 410 caused weird behavior where the APN would not be saved.
I wound up deleting all other APNs due to weird behavior of the phone in saving/not saving the APN values I painstakingly entered. Part of it was the problem I mentioned where changing the MNC value would cause the APN-in-progress to simply disappear from the phone when you chose to save it.
Now I'm finally able to text pics to my young adult children who live in different cities!