I'm also afraid anything in the attic, regardless of size, will provide reliable reception of the DC channels. The
absolute minimum antenna I recommend would be the
Winegard 7694 mounted at least 5 feet above the roofline. The
7696 recommended by Electron would be an even better choice if at all possible.
The Winegard 8700 preamp is a good choice & will help with the DC channels once the antenna is outside.