Hi and a warm welcome to TE (even if this isn't your first post).
I also experience the full stomach situation, and that's okay because my stomach is small. I just fill it more times every day, so basically I usually have about 5 meals a day. Even when I am really very hungry I can't eat very big quantities, but I wait until I can eat again and have significant snacks (combining carbs and proteins while avoiding fat, which takes care of itself) through the day.
As you cycle more and spend more energy you'll probably get crazily hungry. Last year was my first year on the bike and boy! did I eat. I don't notice it as much nowadays but I know I eat more than the average chickie. This being said, 1500 calories as a base is not that bad. Do make sure you intake some fuel on the bike though, as it has been said already...
And, by the way, don't freak out if you gain weight. That's muscle. And it's good for you.