Gentle Persuasion

The giant stronghold provides a good location for a long rest, even if the players decide to stay for a couple of days in order to fully recharge any expended hit dice. The doors can be barred, and most rooms inside barricaded against intrusion. If they stay too long, or if you want to give them something to deal with while they recover, have a war party of orcs arrive during the night. They approach the towers, and will pause on the near edge of the bridge to await the challenge from the orcs guarding the doors. When they hear nothing, two of them will approach to investigate, and they will try to work their way through the tower to ferret out any intruders.
Setting a watch at the top of the tower will give the party a heads up (perception DC18 to notice their approach, an opposed stealth-perception check if they don't to notice them investigating). The party would have 5 orcs and 2 captains. More or less is fine, the point is  to keep the action alive during a down period, not as much to really challenge them.
At some point, they will need to get back on their journey. To that end, a flyby with the dragon might be in order. Sensing a disturbance in the balance around its mountains, it comes over to see what is afoot. After taking a couple of passes, it will descend to breathe fire at the courtyard and any exposed therein. Then it will take to the sky flying up the river, beating at the sides of the hills to bring avalanches of rocks down into the gorge, destroying trees, trails, and temporarily blocking the river. The force of it at this point will quickly open a channel back up, but it could be enough to cause a flash flood and destroy the bridge.
The point here is to get the party moving again, and to encourage them to follow the path across the swamp. Imogene can see the value in the approach shown on the map. While it doesn't lead directly to the dragon's lair, it does appear to show a safe passage through the bulk of the quagmire. The trail leads to what looks like a village near the far side of the swamp, against the eastern wall of the volcano. With that as your destination, she thinks that the map offers a good means of approach. It will take you through a difficult terrain and bring you within reach of the dragon's lair in about a week's time, saving at least a few days off trying to follow the river to its source.
Imogene doesn't know what lives in the swamp, only that it is full of terrible abominations. She is also concerned that it was in the fire giant's possession and seems to direct you to a village. It will require caution to use the map, and may cause further trouble at the far side of the swamp as you try to negotiate the final escape from the far side of the swamp.