Thank you for the reply Carrie.
I do not want to use a mosaic dataset because I need to create a layer to use in regional models and analyses and to share with others that may or may not be using ESRI tools. Also, as mentioned above, filling "no data" areas was not an issue. However, I did end up using focal statistics to smooth out the seam (so marked this question as answered) using the following syntax in Map Algebra:
Con(~IsNull("SeamMask"), FocalStatistics("DEM", NbrRectangle(5, 5, "CELL"), "MEAN"), "DEM")
Where SeamMask is a 200 meter wide raster that overlaps the seam where the DEMs adjoin.
The results aren't fantastic, but it does help ease the transition between the DEMs a little.