I once made a blue & white snowman tablerunner & after I had sewn all the blocks together & put on the binding, I realized I put them together incorrectly! In my eyes they look like a mishmash, but nobody knows what they were supposed to look like, including me! It's been on my table every Christmas for the past 10+ years.
As for your log cabin blocks, I can't see why not using your intended color would be a problem. When I started quilting many, many years ago, I may have taken it apart, but today I say, put it together & finish it. It may not be as bad as you think. And, if you really don't like it, you have a charity quilt to give away.