... but maybe the plane will fly a bit nose-up because it will fly slowly dragging that banner.

Only thinking theoretically, but a banner won't move up and down and left and right like a sailplane, it's just always straightly behind the tug. So you shouldn't have any harm connecting the banner to the airplane's tail. It's even advantageous that it can't tangle, the small down force helps holding the airplane's nose up, and you don't need any special rudder authority either. After all you won't fly turns with rudder but with ailerons, and of course you'll use rudder only to counteract adverse yaw, won't you?

Did you already think about picking up the banner from ground or unreeling it in the air? The other way around: Did you ever see how it's done full-size?