Today my search was over. I picked up a Singer 112W116. It is an industrial-grade sewing machine that can sew two rows of lock-stitch at the same time, 3,000 stitches per minute. I'm not sure how old the machine is, but I'd guess us is older than I am.

I need to see if I can get it to working soon. When I built the balloon I was pretty good at setting the timing on a sewing machine and having it run smooth. But I've forgotten those skills and will have to learn again.