if your strips need to turn corners they will need to be cut on the bias

Now I understand better what you are trying to do. I would do one of two things. Either figure out a "basic" block for the pattern - although looking at it, I'm not sure there really is one. If you can find it, then draft it out, with the longest single-colour pieces you can and make a bunch of those. Or, tackle it one row at a time. Count the # blocks of one colour, multiple by 2 (for 2" finished squares in the original pattern") and add 1/2" (for seam allowance). Cut that strip of the appropriate colour, and move on. You will have a lot of cross-wise seams, for the rows that way.

I made a quilt recently which was designed with 2" blocks, and I split it up into a bunch of square sections, and plotted out blocks of single colour in each, similar to what you are trying to achieve I think. That allowed me to do some larger squares/rectangles, rather than single rows every time.