I've never had a problem with bowing. When I'm done sewing my strip sets, I press them, but I make sure the strips line up straight as I'm pressing. Sometimes I'll use steam and/or starch as I go.

I sew strips together, press and cut to the size I want the border to be. In the corners I usually sew a square. You could miter the corners. I had better luck folding over and top stitching to the bottom piece.

If Bearisgray can do it, it must be possible to keep them from getting wavy. I try to pin the beginning, end and a few spots along the way. Then be sure they feed evenly. Takes a minute to do this, but you end up a lot happier.

Are you flipping the strips when sewing them together - in other words, when sewing 2 strips together. first ends out of the machine are the first to go back in for the next strip. I did a bargello years ago with mom. I started doing that; not a single bow. I tried to explain it to my mom but she ignored me; all went in the same way and it was really quite bowed. She was stubborn and I guess since she'd been sewing long than me, 'mom' knew best.
But the flipping end to end as you sew does help eliminate a LOT of that bowing. Hope this helps.

I'm guessing you've tried all these suggestions by now and don't need any more advice?

So I won't give any on the SEWING/BOWING , but I did just think to add this: if you decide to subcut your long strips to shorter ones before sewing again, make sure to measure your sections so each is long enough for the block size.
It'd be a shame to cut willy-nilly and then find out some are short by 1/2" . But you probably knew that, so forgive me if my comment insults your intelligence. I consider myself bright, but I've done some really dumb things by not thinking. Many of those things are measuring/cutting related! Just want to save a lot of time and aggravation for you if I can.

THANK you!! All of you!!

I am not offended by anyone's comments. All of us have various talents, knowledge and experience. There is no way that we are going to know what each of us can do or not do.

Personally I'd rather that someone explain something than not say it because they figured I would know it!

My piano keys are done. I've spent the day sewing the inner section of the quilt. Now work gets in the way so I may not get back to it until next Saturday! Once it's done I'll post a photo of the flimsy!

Thanks again ladies!