I am a great believer in saving assembly time. Especially if you get the same results either way. As for randomness, you could always take out a few squares from the blocks that were stripped pieced and insert one of the other color squares.
Note that i love random when other people do it, but it makes me crazy when I am piecing a quilt. I'm not particularly neat and orderly, but when quilting it seems that random-ness doesn't pass my personal fun to do test. It is possible that my color vision challenged self is constantly second guessing random placement when piecing a quilt.
