I always assumed the DR bypassing effect was cumulative.
+3 for silver/cold iron, +4 adds adamantine to the list, +5 adds alignements.
So I'd say in your example, the sword does indeed bypass the beast's DR.
And while that means Silver and Cold Iron do become redudant eventually, you've probably had your weapons for a bit by then and made good use of them anyways. Not a big loss.