I have found my solution in a quilters guild. This weekend, I went to my first gathering of a Modern Quilters Guild (i.e. most everyone was born after the Great Depression). I packed a half dozen unfinished projects to take with me.
I had a great time meeting the amazing quilters who were there, and being able to work on my projects for a few hours. Screw trying to quilt at home. For now, I am just going to dedicate one day a month to quilting with these ladies.
I cut all of the pieces into the requisite diamond shape (there are plastic templates you can buy for this). Then, I ironed all of the pieces on to a backing material using double-sided fusible interfacing. I then used a zig zag stich to sew all of the pieces permanently to the backing.
If you do not mind the look of the zig zag stitch bordering each piece, then this is a great way to complete a quilt quickly that would have otherwise taken me months!