I wanted to keep data turned on but limit it to MMS traffic. If possible, I wanted to be able to flip a switch and have regular, general purpose data work, too. That would be mainly for when I am somewhere with no wifi.
I found a few key things.
First: hang on to your working APN settings, but delete "default" from the APN Type field. If that is there, data will use that APN even if you have the radio box toggled OFF.
Second, add an APN just like your main working one, but make the APN Type field mms, and nothing else. When you save that, you'll see that it doesn't give you a radio box to enable/disable it.
Now, if you disable the original APN by checking the radio box and making it empty, you can try sending yourself or someone else a test image by MMS. You should find that it works.
It's a good idea to try browsing or doing something else that would use data to confirm that other data is turned off (disable wifi, too, for that test).
I installed an app called "My APN Switch" to let me switch to the other APN without drilling down through the settings menus. I have no connection to that app but it seems to do what I was hoping.
Please test this thoroughly: I don't want to give you bad advice that makes you use data unintentionally!