It seems like a considerable issue to me, the fact that the cards move around a lot.
I found the same. The solution is simple: use a felt playing surface. It's a big improvement, solves the sliding problems, and has the additional advantage that you can also use it for other games. It's relatively inexpensive from most fabric stores. I use a felt Roll-O-Puzz puzzle mat, which works equally well.
For a previous discussion on this problem and more suggestions, see this thread:
Problem of sliding cards and slippery playing surface?