I started a large lone star YEARS ago. Sewed on it with all those bias little bits until the star was done. Stepped back and went "OH SH*T" - apparently I had turned the first piece the wrong way so instead of a nice gradiation, mine was going the wrong way. It is still in the tub and I will have to finish it some day. After getting really mad at myself, I now simply accept that it "meant" to be different.
Your idea about the random placement sounds good. You can also post a picture and I bet you'll get even more suggestions.