I always embroider my blocks first as well. I think three layers are too thick for your hoop to get a nice flat design. It maybe possible to stretch your hoop with 3 layers, and it may not want to tighten down when you do a single layer block (+ Plus stabilizer). Your going to have all the thread showing from the back side of your quilt.(?) Sounds like it will be a lot of seams to stitch together by hand as well. (?)
Good luck with your project.