New Bearings

The experience in the tunnels will eventually lead the party to the shelf. Once they reach the top and defeat the main guard, they will be able to exit the mountain and be on their way. The main kobold army is away, but they will return eventually. The party need to get going and be on their way, before they are overtaken. If anyone has Survival, they can roll a DC15 check to get their bearings.
The kobolds have taken them several miles up into the mountains away from the river. Indications are that the bulk of the kobolds have continued even further into the hills. You are able to find evidence of a trail leading down into the valley. Perception DC18 will understand that the trail is likely to be watched. If they take care, the party can avoid detection with successful DC15 Stealth checks when they pass a lookout. There are three watches on the pass between the cave and the river. Each watch consists of 8 kobolds. Once all three have been passed or defeated, the party can find their way to the river without further incident. They reach the river about a mile south of where they went up into the gully where the stone giants were. They can make their way upriver and back to the fortress if they desire, or continue on the way upriver. They have lost their boat, unless they took care to secure it at some point and go to that location.
As a game master, you have multiple options. I like the idea of using the fortress as a base for excursions into the hills, and as a spot to defend on occasion. There is still a need for experience, and the fortress offers a lot of good options. I don't know that they need to be written out as much, the beauty of the location is that the encounters can be random.
At some point, it will make sense to drive them out and get them on the move again. If you choose to do so at this point, have kobold-themed groups come after them, looking for them. Throw in some ogres, bugbears, hobgoblins, etc. and the threat will eventually put some pressure on them to get moving.
The key to this episode is the movement of the party past the watches. The options I gave above are good for a quick escape, but they could be fleshed out to fit your interests and desire. This is a good opportunity to explore more of the story telling elements of gameplay. The barrenness of the hills, the steep trail and sketchy looking rocks leaning against the cliff... a good chance to play up the scenery. If they fight or don't fight, its less relevant for this part.
I like the idea of them going back to the fortress. I think it would make a good location for a proper send-off encounter, with an army and powerful monster. Something grand and glorious to really tax their resources, and bring the place down in a pile of rubble. That would be a good reason to start moving, and fast! Something to ruminate over.