You can use your beer bottling procedure with a few differences:
1) depending on the final gravity, you may want to backsweeten it if it’s too dry (assuming you don’t like it that way). I don’t know much about which iteration of the JAOM recipe you used, though if you used a champagne yeast, it might be super dry. If you add more (warmed/dissolved with boiled water) honey to your bottling bucket to backsweeten it, you’ll have to also add some chemicals to prevent the yeast from eating those sugars. Most people use a combo of potassium metabisulfate (campden?) and potassium sorbate, I think. The exact amounts will depend on your bottling volume.
2) if you are cautious and concerned that the above step didn’t stop the yeast, you might want to bottle into champagne bottles with corks (you can get push-in plastic ones and wire cages if you don’t have a corker). At the very least, use heavy glass beer bottles if that’s the route you’re taking instead.