The lowest contours shown on the Topozone maps are 3350 for both the Arkansas and Republican Rivers, although the width is much greater at the Republican. Since there is an official publication (Elevations and distances in the United States by the USGS), I think we should stick with the Arkansas for now. It should be possible for someone to visit both points with a GPS. Any local takers (I am in Arkansas and don't have a GPS anyway!)?
However, Fred is correct that the Arikaree is even lower. There is a contour at 3330 and a point at 3321. This should be GPS'ed as well.
Thanks for a great job.