Christine, you sound like myself. When I got my first tube, I had a nurse come over 3 days in a row to make sure I knew how to use it and how to take care of it. She gave me the same instructions that you were using, Neosporin around the site, gauze around the base of the tube, under the device that kept the tube from going into the stomach further, and then she had me tape the part where the syringe went in, to my chest and above the hole in the stomach. I had never experienced a spill that I myself, didn't create. Like when the syringe came out of the spout while feeding.
A nurse acidentally pulled the tube out at my last hospital visit but they replaced it with a Mic-Key low profile tube. It is only 24 French in diameter but it works well. The tube I use now would fit inside the other tube. I never used the syringe with the plunger before now, but now I use it all the time. One thing for sure, you won't get a cheese burger through this one!