Numerous applications of ammonia solution don't seem to have got me any further forward.
(For those joining us late, I've reached the point where, with the seatpost head in the vice, vigorous heaving on the frame will rotate the seatpost, but not get it out of the frame).
I've drilled a hole through the head of the seatpost, threaded it, screwed in a length of M8 threaded rod, and tried the giant corkscrew arrangement, albeit with a rather weedy, thin-walled bit of tube. The tube collapsed rather than the seatpin shifting. The principle is sound, though, so I may re-visit that if I can get some thick-walled tube of the right inside diameter.
Shocking force might help, I thought, but hammering on the seatpost head isn't applying force exactly along the seatpost axis. What was needed, I thought, was a slide hammer. So I threaded the head of an old lump hammer onto my bit of threaded rod, screwed on a big washer and a bolt, and, with the bike upside down, thumped away with the lump hammer head sliding along the rod and banking against the nut and washer.
The seatpost may have shifted a millimetre or so. Or I might have imagined it. It's going to be a long job getting it out that way anyway.
So at lunchtime today I'm going to an old-fashioned hardware store in Stamford Bridge to see if they have any caustic soda.
I'm beginning to suspect that, whatever the state of corrosion, the seatpost is actually the wrong size, compounding the difficulty, and that I'll probably have to use the giant corkscrew or slide hammer approach even after the application of caustic soda...
Or saw it off and saw slots down inside its length with a hacksaw blade... erk.
Rest assured, if I get it out, you'll be told.