I guess I don't understand not wanting to piece borders, unless it's imperative -- for some reason I can't think of -- that each border length be one continuous piece.
Quilts are made up of seams, after all. Seams in blocks, seams attaching blocks, attaching rows, attaching borders. Seems (pun slightly intended
) that this is what makes up a quilt. Seams in borders don't bother me, as long as they are not awkwardly spaced.