I do all 3, by hand. Quilting or tying. FMQ on my DSM and taking it out to the LA. Each has its separate purpose and meaning. Tying is great for crazy quilts and charm quilts. Quilts that I have done as patchwork can be FMQ or LA depending on the quilt. For a small project like this I would do a DSM and maybe some ruler work if possible. This sounds like it was a fun project.
I am always looking for guild projects to do and t his one sounds like it was fun.