Your first swirl is up! Woo!
Use the news print to draw more swirls in the areas in the plans, and keep mounting them on your wall. After a while, I stopped using the newsprint, since I had an idea of how large the swirl would be and just drew them freehand on my ConTact paper backing.
Also, don't worry about the middle of the blob while making the swirls. The swirls are essentially the outline of the blob.
I kept working my way around the room, to make the full outline. I then added a layer of smaller swirls, made from scraps, to add interest and scale to the design.
When you're happy with your swirled outline, cut out scraps to patch up the center area, filling in the area you ignored. My seams weren't visible once you were 6" away from the vinyl, so I really just patched it up with whatever pieces were left. The only part to pay special attention to is having the connection points curve smoothly into each other, so a bit of trimming on one side or two of my sloppy patches would have them fit nicely.