Your rows look beautiful even with the curve. It looks like the white on white is a less dense fabric than the boxes? Since you know that the white needs easing in, put the white on the bottom next to the feed dogs and sew two strips together. After sewing the two strips together iron and measure the two strips together and see if that has corrected the curve enough. If it has, sew the strips together in sets of two with the white strip always on the bottom and alternating sewing from the top down and the bottom up to further minimize curving in all the twosies. Re-evaluate at each stage of construction.
OR--You could also mist your strips and block them straight before proceeding. Find a large table and cover it with a surface you can pin to and draw marks of where you want the strip to measure. Mist a strip and pin it with non rust pins to the outline and let it dry in that position. This may correct the curve but make sure before MISTING that you don't have any bleeder fabrics.
OR--You could replace the white with a denser fabric but even then that doesn't guarantee you won't have the same problem and would be a heck of a lot of work!!!
OR--maybe someone else will give you a better idea, good luck.