Alpheus, I'm not sure if you've already solved your problem or not but I would recommend against converting your DEM to a 16-bit raster. This is very likely to reduce the precision with which the elevation data are stored and can be very disruptive for any subsequent analysis, e.g. flowpath modelling or slope analysis. If your data are currently floating point, and I don't know if they are, then this conversion will also result in a degradation to integer values, i.e. nearest metre or foot. If you are finding seams between your tiles despite all of them having the same display minimum and maximum values, then this could only be caused by a different binning strategy among some of the tiles, e.g. you might be using an equal area stretch or something similar for a few tiles. However, given your problem is mainly with display, you might consider mosaicing your DEM tiles into a single larger raster. That way their colour ramp and display parameters are guaranteed to be the same throughout. There was a similar question to this a short time ago,
Is there any way to 'clean' up ASTER v2 DEM data?
That person found that mosaicing was the solution to their problem with creating a seamless display of elevation data.