The easiest way to do this is in arcpy using the Geometry object. You can create a feature class, create a bunch of geometries, and copy them into the feature class using Copy Features.
also, where is the 'centre-ish' feature with respect to the dimensions and as Blake indicated, its orientation?
Just thought it might be easier to produce the shape, place it about a 'central' point, then translate and rotate the resultant into its final position.
Dan, I like this idea - create the buffer about 0,0 and then write and use a little function to copy the template buffer poly and shift/rotate the xys into place for each point.
If you need code to rotate XYs there is a function of mine in this thread. The code also has code to use the function to rotate a polygon. Not as easy as one would hope. bixb0012 is on to something with his idea https://community.esri.com/ideas/10963!