Removing a frozen post from a carbon frame is very different than if the frame was steel. The carbon seat tube won't take as well as a steel one to most of the brute force options.
My suggestion is to pay a decent shop to ream it out with an
adjustable blade reamer. You'll have to do some prep work with a half round file to create a taper or bellmouth at the inside top so the reamer can easily pick up the axis of the seatpost and follow it down.
Most decent posts are concentric inside and out so once you establish the alignment, you can take off a few thousandths on each pass. As you near be vary careful and sight down the tube after each pass to make sure you're not breaking through one side and reaming the frame.
BTW- you can do this yourself, but you have to factor the cost of one or possiblw two reamers into the cost. Measure the current post ID, and the final ID, ie. 27.2mm and see if you can find a single reamer with the right range. Metric or inch doesn't matter as long as the size range is OK.