Players ride home is toast - seeking ideas!

Hey all! I am lucky enough to be DMing for a group of close adult friends playing 5.5e. They're an awesome, engaged, and fun group. Recently, they have gotten themselves into a bit of a pickle:

The party has encountered a cerberic (3-headed) dragon turtle (CDT) that has been disrupting shipping to the benefit of the local pirates. Their ship is an artificers marvel and it can walk. Important because in their stand against this much more powerful enemy, they chose to place themselves on the second floor of a massive stone giant constructed tower and to block the front door with their ship. The CDT is a siege monster, so just ended up ramming its way through the ship. The session ended with the CDT pursuing them into the tower.

So, here's the pickle: their ship is fucked and they are a 5 day sail from the nearest civilization. The captain, an artificer, could fix the ship, but for the sake of reasonable narrative, I think it should take quite some time (like 2 weeks).

My thought is that they have gotten themselves into a survival situation. Food and shelter is limited. The area is dangerous (pirates which they have already encountered, tons of monsters, etc.). My thought for game play is to gamify the pursuit of food and shelter and to throw baddies at them until they get the ship repaired. Struggling with how long to draw this out... I think something relatively expedited.

I am trying to avoid deus ex machina. Does this suggestion seem narratively reasonable AND fun game play? Any ideas on how to make it more fun??