I also prefer borders cut along the selvage, but.....for the times when there isn't enough fabric to do that, or the borders are pieced for whatever reason (by design or by necessity), here's a secret trick I began using many years ago to keep the outer edges from having any "give" and wave.
TWILL TAPE! Sold by the little package along with hem tape/rick rack/blanket binding at Joannes, etc.
Apply it IN the outside seam allowance (under the binding).
Jan in VA