Cellular data not working since 5.1 Lollipop flash
I'm back up and running.  Here's what I know at this point.  I'm posting it here because I think many people may experience the same behavior.

After much back and forth with Simple Mobile (note that they share some infrastructure with T-Mobile, Tracfone, etc., so users of those services may be affected as well) they found that my cellular data had been disabled on their end.  Nothing was wrong with my account, indeed, voice continued to work normally, it was just the data that had been disconnected.

I asked why this happened and the 2nd-level support person told me that they are still investigating but one thing that's possible is that a change in 5.1 Lollipop caused something to fail on their end.  She said they have been receiving numerous trouble calls with the same symptoms, all with phones recently upgraded to 5.1.  

So, allowing for the typical misinformation that we all get from customer support, this actually seems like it's plausible.  I don't want to spread misinformation, but if anyone else is tearing out their hair with these symptoms, try leaning hard on your carrier to check your line.