I think you would be better off if you stitched your design directly onto a firm tear-away stabelizer, then glued the embroidery to the paper. Most machine embroidery designs are so stitch heavy, that they would just tear the paper.
Rent a rear tine roto tiller. After you get the beds worked up, start working compost into the soil, until you have the consistency you want. After you have the bed planted, remember to mulch. Grass clippings are good, because they will decompose, adding to your good soil.