The Nebraska event you're discussing was 12 Jun 94 over Norfolk. John Hart and I observed that storm for over 6 hours, including the infamous connecting-funnel vortex over Norfolk that appeared on one of the TVC tapes. Our view was from about 1.5 miles to its SSE, whereas the Norfolk resident saw it almost directly overhead. This was one vortex with condensation extending in a U (or, for college football fans, a Miami Hurricanes logo) from the ambient cloud base. Since the vortex axis was bent 180 degrees along a vertical plane, one end was cyclonic, the other anticyclonic.
My slides of that middle/mature stage near OFK didn't turn out well at all, but here is how that supercell looked about two hours later in fading daylight...
http://www.stormeyes.org/tornado/SkyPix/westptne.htm
That was taken near West Point, about 5 hours after the storm's 3:30 p.m. initiation in Antelope County.
We had driven from KC and were at the old Norfolk WSO, analyzing surface charts, convinced we were in the right general area, when the storm blew up to the W. We stayed with it -- at a slow, leisurely pace and on great roads -- for the next 6 hours. Our last view was of the slowly rising and shrinking stack-of-plates, silhouetted by lightning that pierced total darkness N of Tekamah.
The storm was not tornadic, but that doesn't matter. It still ranks among my top 3 or 4 favorite intercepts of all time for combination of absolutely nailing the morning forecast, the remarkable longevity and sustained beauty of the storm, and almost laughable ease of observational strategy. That's a very rare combination!