With any luck, you'll have been replacing the moldy bits with Whale Tallow Soap before it's all gone!
Wouldn't it be cooler to replace them with, say, steel or rock? And wouldn't miasma kill the fort's happiness?
Legendary whale soap trumps miasma.
Let's see if I get the plan...
Wait for multi-hundred-ton whale to beach itself.
Strike the Whale!
Mine whale fat.
Turn fat into soap.
Use soap to replace rotting whale flesh.
...I don't think there's enough fat in a giant sperm whale to do that, you'd need to have your Starting Seven make soap 48 hours a day minimum to turn that fat into soap before the whale rotted assuming a sufficient lye supply...
Great idea, though.