Two main bits of advice here. Number one, start really drilling on the Sit-Stay command.
Number two - keep the dog away from the door. Sounds simplistic, but it's the easiest way to solve the problem. This is something that comes from working at a wildlife park. We could train every single animal not to run out of its cage, but that would be a hassle. Instead, you'll notice next time you go to a zoo that every enclosure has what's called an "airlock." This means it has two doors with a space in between. This way, if an animal "gets out," it's not really out - it's just in the airlock.
I have an airlock in my house - the small front room that leads to the front door. The side gate is padlocked at all times unless I need to go through it, so that a visitor can't leave it open and let the dogs out. It's an airtight system.
Make the room that leads to the front door an out of bounds area for your dog. Create an airlock. And work on that Stay command.
