That got me to thinking. By using only the Moon's orbital period I computed that the Moon moves through about 43,942 arc-second per day, and that ought to be the slope of the line through perfect data. I compared that number to each of the line slopes to see if one of the slopes was much different or if they has similar differences. I was able then to isolate one set of observations for further study, because one slope was much further off than the other. The data from Weems was further off despite his more sophisticated timing methods.
Theory can help identify the data to examine more.
I did spend some time pondering the reasons that Weems' data showed longer times for the drift measurements. The probability of having a deficiency in the WWV signal was ruled out. The probability of having a slow stopwatch was also ruled out as being improbable. Field rotation in Weems data, but in my data I had effectively removed it. As of today I am working to remove the effects of the field rotation from the observed data.