holly I turn the vase upside down so I don't have to worry about water getting into it. I make sure the ground is flat where I put them and they are so close to the ground I do not believe they will fall over. Even if they do the E-6000 if you use enough will not come apart. I made a shirt about 10 years ago with it and it washed atleast 25 times over the years I had it and the flowers and beads didn't move. I didn't dry it but that is because it was covered in silk flowers and figured they would ruin.
You could buy a cap for the end of a Pvc pipe and glue inside with pvc attached and push it into the ground. you probably would have to push a piece into the ground to make the hole so easy to push it into. You could also fill the vase with small stones and then seal them into it with caulk. that way you could still use the vase upside down. I do all my vases upside down because the one my friend gave me in a stack filled up with water.
I like the idea of filling with stones for the color effect it would give the stem. Remember you will be adding alot of weight doing that. I am saying that because carrying it to and from a trade is more apt to be broke. 2 of my mushrooms are actually crystal decanters right side up. The decanters are heavy because they are crystal. But everything is also a matter of how much you can get it for. The blue bowls I collected years ago as I love blue glass of any kind.