It appears that there were two different problems. With Ahmed from ESRI Customer Care, I figured out that something was wrong with the first copy of the table. I made a new copy of the EROM table into SDE and that helped. Unknown what was wrong with that first copy. But we also found out that when making the Join, I had to check the box to use the "Keep only matching records" option. If either the feature class or the table was from the file geodatabase, "Keep only matching records" was not necessary.
The NHDPlus Feature Class is a line feature class with 272340 records. The joined table EROM has 238811 records. But there are 39529 records in the Feature Class that have no match in the table. I didn't know there were that many mismatched records. I had to run the selection again to be sure. These unmatched records with a null value in the graduated symbol item seemed to upset the drawing in the SDE feature class - SDE table drawing, but the other pairings were not as sensitive.
I did some further testing with the complicated graduated symbology and differences in draw times with SDE and File Geodatabases.
SDE Feature Class - SDE table - Keep Only Matching records- draw time 9.7 seconds
SDE Feature Class - FGDB table - Keep All - 58.0 seconds
SDE Feature Class - FGDB table - Keep only - 51.7 seconds
FGDB Feature Class - FGDB table - Keep Only - 44.7 seconds
FGDB Feature Class - FGDB table - Keep all - 48.3 seconds
These are the kind of performance gains I was hoping for with SDE! I'm glad it works.