Thank you for the warm welcome, folks!
feline fanatic - Thank you very much for your suggestions. It makes sense that SITD would be good for keeping the points in the spot light. I enjoyed looking at all of your quilts, and the Agave Garden one made my heart sing! Love the colors, the design and especially the quilting. I really liked how you completed the lone star diamonds by quilting additional diamonds black-on-black - a very sophisticated look! I also liked how your dense quilting in the center of each diamond really made the outer part of each one really pop out. Did you get all that puff with a single layer of batting?
Kitsie - I appreciate your suggestions, but I am looking for suggestions for the *quilting*, not the quilt (piecing) pattern. (I think it is unfortunate that our craft does not have a term for sewing the layers of a quilt together that is more distinct from the word "quilt". I have found that it is difficult to get on-line searches to focus on the quilting aspect, as opposed to the overall quilt creation.)
Because the Lone Star quilt pattern creates such large areas of background in the set in squares and triangles, I am considering making smaller stars for the squares and half stars for the triangles. A really nice example of this is Wimbledon Star on page 38 of Lone Star Quilts by Jan Krentz. After I finish piecing the central star, I'm going piece one of those stars and see how it looks with the main star and the background material. If I go ahead with idea, I will probably also copy the idea from Wimbledon quilt of quilting a mini Lone Star in each of the set in squares of the smaller stars (and half a star in each set in triangle); it's a neat way to repeating the star motif in the quilting. (And it is easy to do with a walking foot!) The down side of this whole approach is that it add significantly to the amount of piecing - the main star is 8x8 one, so that's 512 diamonds. Adding smaller stars means making a bunch of 3x3 diamonds, so that another 432 diamonds. That's a big addition! (The smaller stars would also use diamonds that have a finished size 25% smaller than the main star.) At this point, I have 25% of the main star pieced, so I will see how I feel about the additional piecing option once I've completed the main star.
This is about what the main star, background and borders will look like:
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Some of you may recognize it as a Jinny Beyer Lotus quilt, minus the applique. (Jinny Beyer's applique is lovely, but I know I would NOT enjoy appliqueing huge number of pieces her design calls for. I'd much rather do piecing.

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If any other folks have comments on what they like to see quilted on precisely pieced quilts, I'd love to here it. Thanks again for the input.