I'll trust your judgment that there are problems with the quilt, but from here it looks spectacular.
If it weren't already completely pieced, I would suggest quilting it in sections. You could still do that using the method where you divide the batting into thirds. I haven't used that method, so I can't give all the directions, but it's explained in Marti Michell's book Machine Quilting in Sections. You can probably find it online too.
I do think the big stitch would look great on that quilt, but I don't have experience with that either. Big stitch reminds me of sashiko, and I did have a class in that and enjoyed it very much.
My other suggestion is to wait a week or two and see if your feelings about the quilt change. You may find that you like it a lot better when you've had time to forget where the oopsies are.
I have a lonestar kit from Craftsy too (not the same one) and am dreading starting it. The directions aren't for strip piecing, but for cutting and sewing individual diamonds from templates. Sheesh! I'll have to try to figure out how to bring the pattern into the modern world.