looking for your help on this one...

So I have this road bike with carbon fibre frame bought second hand and the seatpost is stubbornly seized inside it.

I have tried spraying generous amounts of normal lubricating oil and penetrating oil from both sides (top and bottom of where the seatpost meets the frame, reached the bottom by removing some screws to gain access to the inside of the frame), this was done several times over the space of a day and even leaving it sink-in overnight...

I have also tried heating the frame pouring hot water as I've seen in some online videos, on top of that, I have also tried heating the frame with a heatgun at a relatively safe temperature (the heatgun has a digital dial to control it).

I have also tried melting silicone on the nose of pliers and grabbing the seatpost with them, there was some grip but not enough to unseize it, the force being applied was so strong that the pliers eventually went through the dried silicone leaving some cosmetic marks on the seat post, so I had to stop to prevent more damage.

Additionally, when I try grabbing and turning the saddle to unseize the seatpost, the saddle railings on the seat rail clamp come off, making it impossible to continue turning unless I put the railings back on the clamps and tighten them; needless to say, no matter how much force I apply, it's always the saddle railings coming off but the seatpost doesn't move a millimetre....

None of it has worked so far, but I don't wanna give up.

I've been reading some literature regarding this matter online and tried to work out the logic of way number 14 on this website (https://www.sheldonbrown.com/stuck-seatposts.html) but I don't quite understand how to do it. It might be the way!

I'm attaching some pictures of the frame and the seatpost with as much detail as I can.

https://imgur.com/a/7sOfFje

Look forward to your suggestions and help.

ps. cutting off the seatpost is not quite an option at this stage.