I think sewing the squares together is going to be even more of a bother than making squares.
You just have to always have a ball of black or yellow with you and make a square whenever you get a chance to sit down.
Then when you get up to sewing it all together, take the time to sit in front of a movie and just get as much done as you can in those 2 hours, then watch another movie in the next few days to finish it off.
My mother reckons it's easier to use single crochet to attach the squares together than to sew them. Attach them in strips and then attach the strips together.