I raided the craft closet and discovered that I had everything I needed - balloons, embroidery floss and glue. (The comments on that link said glue could be used instead of the starch/flour mixture. I figured I probably had the liquid starch somewhere, but I didn't feel like searching for it right then.)
I was unable to fit any candy into water bomb balloons, so I just wrapped the empty (but air-filled) balloons with the glue-dipped floss. I had a larger balloon (the 9" helium-quality size) into which I could fit some candy, so I used that as well, but only blew it up to 4" or so.
I discovered the kitchen chandelier made a decent hanging rack, where they stayed overnight.
After a stop at the store to pick up some different balloons and some actual Easter candy, I tried again. These balloons came in a package with the party stuff at the grocery store, and I was able to fit three Hershey eggs inside them, although not without difficulty. First I used the pump to inflate the balloon, then deflated it. The candy kept rolling around; balancing it on the top of the funnel helped. (Later I used the lid of a highlighter, because the funnel tip was still too small.) I'd stretch the balloon opening over the propped-up candy to get it into the "neck" of the balloon, then inflate it until the candy dropped inside, repeating those steps twice more. The last step was to do the actual inflating and tie the knot. I thought I could do this step ahead of time, but it's a good thing I only did two, because the next morning those two had deflated. So I learned you need to wrap soon after filling.
Working with the glue was really sticky and kind of frustrating, so after doing a few more eggs, I hunted down my starch bottle and decided to give that version a try. I wrapped one egg in plain starch and another in the flour/starch mixture the original poster suggested.
When I checked them the next morning, they didn't look so great. The plain starch one held its shape; however, it just felt fragile and the end of the string needed to be glued down so it wouldn't unravel. The one with flour had just collapsed and fallen apart. Maybe it was the balloon's fault; maybe not. Either way, I decided to stick with the glue method.
The easiest way to do this was to pour some glue in the bottom of a bowl, unwind the floss skein into the bowl, drizzle the top with some more glue, and then start wrapping. Since I was doing 20 of them, I actually reached the point where it wasn't quite so sticky and frustrating.
I didn't have enough cupboard knobs, but the cookie cooling rack worked just fine.