You can read my trauma here. In short, I had a local bike mechanic, with a good reputation for removing posts, cut it out for me. This worked out a fair bit cheaper than posting the frame to Lancashire and I’m pretty sure that, even then, the post would have needed to be sacrificed.
Yours is slightly different however as where my post cost £20 to replace, yours is more like £200 and I’m guessing you’d rather not hacksaw it off if you didn’t have to. From my own experience, I tried everything to get mine out and nothing was shifting it. Even then, I was applying as much twisting force through the post as I dared apply on a carbon frame, but with a Reverb, I’m pretty sure that this much twisting force would have damaged the post.
In short, I’d probably send it straight to the man in Lancashire if he thinks he could save the seatpost.