Why is my sewage ejector pump running so long?
OK... so the mystery has been solved. :-)

The problem got so bad today that the failure rate reached 100% (every time the pump came on it would churn for >30 seconds)... I got a lot of text messages. When I got to the pump, I noticed that during these failures there didn't seem to be any flow at all, and I could feel the pressure build up around the coupler just below the flow control check valve (the one above the ejector pump). 

I began to suspect the issue was with this valve, so I took it off and found it was basically just a disk inside a cylinder.  It was not attached to anything (no hinge to keep it from flipping over freely).  This effectively made the valve stop flow in either direction.  I guess that the valve was originally something like this:



The issue may be similar to the issue described in this video, except my valve (American Granby SPCV200) was a swing check valve:

https://www.youtube.com/watch?v=W65Si-PhMDk