The cell towers could be a problem, especially if they are in front of your dish. In the days of analog, TI was easy to identify on the TV screen. With digital, not so easy. I don't know how it could be confirmed as interfering, without laboratory equipment. But since you say you get signal, but low Q,
Here's something to try, to see if an amplifier will improve the situation. Bring the STB and a TV out to the dish, If you get good Q there, an amp should compensate for the loss between the dish and where your setup normally is. If it doesn't get good signal at the dish, an amplifier will not help, it may actually make it worse.
I still think your solution is a larger dish. Might also fight any interference, as it will gather more signal from the sat. And if the dish isn't pointed towards the source of interference, might just be enough to get the sat signal above the level of the interference enough to get good Q.