Apologies for resurrecting a bit of an old post, but did the BB survive the process in the end? I'm about to do this to an old Specialized Hardrock I have as the hacksaw method has failed, I don't have a BB tool and even if I get hold of one, I'm expecting it to be a bit of a sod to remove!
You could saw the seat post off, cork the open end, flip the bike over and put the caustic though a bottle bolt hole. once you have thinned the post down a lot the ring the cork is in should come out easy.
I recently removed the remains of a seat post that had been hammered down the tube, I took pictures while I did it and video. I will sort some out if any interest.
Might be worth a go if I can get a funnel, would have to use something other than a cork to bung the end though I think, there's several slits running down the length of the post from where I sawed it so presumably it would run down these and around the cork. It'd be nice to know if the bb housing was sealed from the seatpost on the bike, then I wouldn't have to worry about taking it out, or trying to pour caustic into the tiny bottle cage bolt hole!
Would definitely be interested in those. How many times did you refresh the caustic soda solution, and over how long?