Fun concept! Lovely art and character designs. There are also a lot of nice touches like the props on the table and the fact that objects become transparent when someone's behind them.
It was a little hard for me to play since I often couldn't tell whether my line was actually damaging enemies or not. However, the list of planned fixes all sound great, and the use of the theme was perfect as well. It'll be great to see where you take this one.
This is just a random idea, but I wonder how it'd be if the movement tied in more with lines. Perhaps you move AND attack by drawing lines? That could kind of combine the movement, lines, and dash attack into one.