Friday was consumed with a few trips to Home Depot to attempt to improve the sump pump situation. Things got a bit better but still weren't great.
Today we had a tree in the backyard taken down (it was somewhat rotten and in danger of collapsing on its own) which required that the power be shut off for a while. We were worried about the sump pump which had been running about every fifteen minutes so we had a backup plan involving buckets and bailing. The plan wasn't needed when the sump level stayed fairly consistent with the power off. Once it came back on I changed the float configuration so that it shouldn't run as often. Still trying to figure out an explanation for the behavior we're seeing.