@littleK you know it mate.... so relieved, gave it more thought and decided against drilling it with your 25.4mm drill bit.
@ffm thanks, that's an interesting approach, that instrument mouthpiece tool reminds me of a bearing puller. Yeah chuffed I managed to get this out, it was an absolute ball ache, and took some Mcgyvering!
Here's what I did, it was a saga, but maybe someone can benefit from my experience:
Firstly having stripped the bike down completely only then I realised the carbon post was seized in the alloy frame, so went ahead and sprayed some Plus Gas penetrating fluid through the seat tube bottle cage bolt holes and left the frame inverted for a fortnight. After daily top ups of more Plus Gas the post still wasn't budging though and I was getting worried that the Plus Gas might be reacting with the seatpost paint/lacquer, causing that or the carbon to swell, but couldn't find any info online so charged ahead.
As the post still wasn't moving and without access to a vice I thought I could improvise using a G clamp to grip the post's alloy rail clamp against a cast iron metal railing in my front garden. God knows what my neighbours must've been thinking....
As the post was quite a nice one I was trying to be careful but eventually the G-clamp bit into rail clamp so I figured the post was toast and gave it some welly. With some careful twisting proceeded by a loud cracking sound the post moved a bit, hurray.
Everyone knows once you've broken that seal it's usually only a matter of time and eventually the post will come free, so I was feeling pretty optimistic, but the post would only twist side to side, and only a few mm at a time, plus I felt if I kept twisting the post by the rail clamp eventually the clamp would break free, as they're only epoxied in place.
I then realised that the rail clamp must have a small alloy insert that sits in the carbon tube, so if I could grip the post in this area the post should hold together under twisting, but the only way I could think of doing this was with a proper vice.
Enter @littleK who came to my rescue and let me use his bench vice. Initially we did the same as before gripping the rail clamp and twisting the frame and did manage to move the post by about 5mm. Suddenly though the inevitable happened and the rail clamp gave way, so whatever adhesive that was holding it in place had given up the ghost... Bollocks!
In hindsight at that point we should have clamped the post at the section where the alloy insert was in the carbon tubing but instead I hastily thought if we clamped the post horizontally along its length rather than vertically we would grip the post better and I could pull on the frame more easily whilst twisting. But horror of horrors this just ended up cracking the post! Everytime we re-clamped the post the tubing would just squash, meaning we couldn't get a good enough grip on it, plus the bench itself wasn't fixed to the floor meaning it kept moving, preventing us from applying enough pressure.
By now I was running out of ideas and thought some method involving cutting or drilling would be necessary, so @littleK lent me a 25.4mm drill bit and the plan was for me to try cutting the post near the seat tube and reaming it out with a power drill.
A couple of days later, and having given this more thought I was leaning against drilling. Firstly I didn't think the drill bit would reach down far enough and was worried I wouldn't be able to get at the remnants of the post, especially any material down deep in the seat tube. If you look at the frame the seat tube has a narrower section which makes contact with the post that's only about 80mm long, then the tube widens. So I thought drilling could leave a loose section of post down in the seat tube.... A horrid reminder and unacceptable.
I figured I needed to know how much post was actually inserted into the frame and managed to remove the loose rail clamp, then by attaching two spokes together using a nipple I fashioned a depth gauge which showed me there was about 270mm of post below the top of the seat tube.... not good news.
With that much post inserted I thought trying to cut down there successfully would be super tricky and I was going to give up but then thought maybe I could use a couple of stems with 25.4mm clamps attached to the post as grips to pull and twist the post out. I thought the clamps of the stems would grip the post from all sides so wouldn't crush it. The plan half worked, but as before the post was only moving sideways as it was hard to pull and twist at the same time with enough force, and worse after a few attempts the stems started to lose their grip, not unlike my own state of mind by this point.
The stems were slipping as the post was still deforming under compression, when I had a minor brainwave and thought I could attack the issue from the inside by using a quill stem inserted into the post with some old flat bars attached and use those to twist and lever out the post from the frame.
Having found a suitable stem and bar combo I hulked out on the post but still could only twist it marginally, and by tightening the stem I could see the post starting to bulge and split. To counter this I used one of the a-head stem clamps to brace the area that was bulging. This was the final set up that I thought would work if I could only get a good enough grip on the post.
Enter my local VW garage who luckily are literally at the end of my street, and with only minor bribing let me use their bench vice. This one was bolted to the ground and having clamped around the post with the quill stem on the inside and the a-ahead stem bracing the outside I gave it the beans and the post started to budge, result.
As the frame was quite elevated it was hard to exert upwards force while twisting, and the whole time I was conscious of damaging the frame, but slowly the frame started to snake up off the post. 30 hernia inducing minutes later the post was out. I used the orange tape to track my progress and the post was tight right up to the end. To my surprise when it was finally out I inspected the inside of the frame and it was really smooth and clean. The only residue was some black powder resembling soot, so I think it must've been the post that swelled.
Anyway, happy ending, moral of the story is always use carbon assembly grease on carbon posts!