Now that I had my first shot under my belt, I made a few changes.
I turned on that 2nd light so you'll see another stripbox reflection coming on the right side of the vase.
I received the black glass (actually a tempered glass cutting board) that I'd ordered so I put that on top of the stool and underneath the vase. Now we get a slick reflective surface with a nice reflection under the vase.
I changed up the background lighting so that the gradient flows from bottom-to-top instead of right-to-left. I did this by removing the strip box from my speedlight and placing the speedlight below the stool on which the vase was positioned.
Here's the new setup. Well, the new background lighting setup anyway. Notice the speedlight on the table beneath the stool.
After adding the black glass to the background, and turning on the additional light on the right, I got this.
At this point, I'm half way done with the assignment. I've created a couple gradients using reflection on the background and subject and I've done a couple different backgrounds. Next up, refraction and texture.