Whalers have been taking care of whale carcasses for ages, it is not like it is a first?
The whaling museum in Nantucket has a fascinating display about a beached whale that died there. Since the museum has examples of the equipment that was used to extract oil, it was decided to extract its oil in the traditional fashion.
One whale corpse yields quite a lot of oil. The highest value was placed on oils that remained liquid even in winter, so the summer's oils were kept until then. They were exposed to the cold, and the portion that remained liquid in each barrel was poured off to get this most-expensive fraction. As weather warmed up and other fractions became liquid, they were serially decanted. By the time summer arrived, only the highest-melting-point fractions were left.
Fascinating place; if you ever happen to be there, I recommend a visit. It's quite close to the ferry landing.
From the video:
> The carcass (…) couldn’t be cut up and then buried because nobody wanted to cut it up.