Before cutting the new fabric, I recommend starching it with the 1:1 solution of Sta-Flo and water. The way I do it, which is very easy, is to use a large wall painting brush to brush the starch solution onto the yardage until the fabric is saturated. I wait a couple of minutes to give the starch time to penetrate the fabric, then toss in the dryer and iron with steam. Only then would I cut the strips.
Also starch the existing panel before moving on. Make sure it lies flat and that the corners are square.
Measure the quilt through the middle. Cut two strips this length. Pin each strip to the panel before sewing. Fold the panel in half and mark the middle; do the same with the borders. Fold again and mark the quarter points. Match the ends and all the marks and pin at each of these points. Only then do you sew the borders on (one at a time). Press everything, make sure corners are squared, and then measure through the middle before cutting the next two strips.
I think if you do this and starch heavily at each step, you will be fine. Just make sure at each step that the top is still lying flat and that the corners are still square.
I really like your design and layout. Good luck!!!