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.:)

I agree that to promote randomness, in future projects, lol, I would cut the long strips into shorter pieces, not just in half. I even do this with scrap strips. I grab 3 or 4 of a similar length, even if it's only 4-6", and sew them together into strip sets. I'll have a pile of many sets of various lengths and mixed colors, all nice and scrappy! Then cut these strip sets into the size I want, most often in this case it's 2.5" squares. Using this technique, and turning the strips different directions, there is little problem with not having enough randomness. If, once in a while, there is a conflict, it's easy to rip that short seam and flip something around.