Are you sewing long strips together?
I would sew them one to the next and flip each one.I would not sew them in pairs. I put a piece of painters tape with an arrow marked on it in the direction I am sewing the first two strips together and it acts a reminder to flip each additional piece. top to bottom, bottom to top. I would sew 6 strips together and check for bowing by laying the strip set on the cutting mat to see if it is straight.
Start with smaller strip sets and if it is going okay then add a few more to the set. IMHO, smaller sets work better.
How wide are the keys you are making going to be?
The bowing may not be an issue at all.