I think there is something else in your code that is messing it up; check this jsfiddle, I copied and pasted your code and only added:
.dragMe {
background-color:#0f0;
}
.preview-holder {
background-color:#000!important;
}
Just coloring them so you can see the widgets. Other than that, the only thing I changed was the text of the buttons and your "...ETC". It doesn't drag if you try and drag it by the button, but you can drag from anywhere else on the widget.
If for some reason you need to drag by the button, I would recommend changing it to a non input/button element and simulating whatever functionality you need with JavaScript.
When my grid gives me trouble, here's what I check:
Opening/Closing tags all match
data attributes make sense (Gridster gets crazy if widgets overlap)
Styles are being applied appropriately - make certain it is supposed to look like what you think.
I had a couple times where I was expecting to see one thing, and because I didn't assumed the javascript was at fault, but it was missing CSS styles.