Dyeing the squares first is the way to go--IMHO. Use procion dyes. They actually bond to the fabric to reduce risk of fading and running. Try Dharmatrading.com or prochem (can't remember their site) in Massachusetts to buy the dyes--which are available in tons of colors--even more if you just buy three primaries and mix your own, mordant, synthrapol, soda ash, etc. I love dyeing fabric and with kids, I love teaching them to dye. Look up sites for techniques, such as swirl or mandala. Dharma has many instructions for this on their site, too.