I was also taught not to piece borders (back in 1982), so I go out of my way to purchase extra length to avoid piecing...though on rare occasions, it has been necessary. When that happens, I usually try to find a creative idea to insert in the border (like blocks the width of the border) that enhance the appearance of the quilt. I would NEVER cut long borders from selvage to selvage and piece them. With large quilts, I also fold the fabric and make one cut to remove the selvage and then another one for each section of border. I have never had a problem with waviness. Maybe it would help to press the folded fabric before making the cuts. Spray starch or sizing on the fabric could help too.