LyndaOh ... I like your solution. I was going to suggest to OP that with Lone Stars it easier to use a darker color in the center to hide any ... ummmm ... mis-matches
The only other thing I would add is that I love lone stars that use the same background fabric as was used in the 2nd or 3rd position down from the point of the star ... it makes the tips of the star 'float'. I've done two like this (actually 1 1/2 as I'm not finished with the second one yet) and I love the effect I get from the "floating" points.
Pic below is one that is finished to show you what I mean by the "floating" point. In mine below my background fabric is the same as the fabric used in the 4th position from the tip ... I prefer it to be the 3rd position though (which I did on the one I am making now). Also note that I didn't use the darkest fabric for the center ... and my mismatched points in the middle are a little obvious.