A few years back, I picked up a Kestrel carbon road bike that had a stuck seatpost at an estate sale. Was there to get different bikes and accessories and noticed that the Kestrel had a free stem but a stuck post. Parts alone were worth what I paid for the whole bike, so sure, why not take a chance.
Now this was a new one for me, how to free the post without damaging the carbon monocoque frame. Post was an American Classic alloy, and the frame had an aluminum sleeve within the carbon seat tube.
What finally worked: Attached an old saddle to the American Classic. Got a small can of Kroil for something like $12 USD. Dribbled Kroil around the post, let it sink in, took a rubber mallet to the side of the saddle and started giving some controlled whacks. Rinse & repeat. Took me a few weeks and who knows how many tries, but it finally gave without damaging a thing.
Supposedly Kroil has a micropenetrant chemical structure and works similarly to the 50/50 combo of ATF & acetone already mentioned. Thought I'd mention it in the spirit of whatever works. Still have that original can and have used it several times since.