You guys. Sheesh.

First get a can of Kroil from Kano Labs. They are online, you can't buy the stuff in stores. Douse that thing with it and let is sit a few days. In the meantime, fabricate a tool from a paint scraper or the like (threaded rod with a heavy washer or two on the end, something at the other end so you can grip it) that allows you to reach all the way to the bottom of the seatpost and catch the tubing with the tool. If any of the seat post is still visible through the frame tube gap I would put a saw cut in it so you have something to move it with.

Then get a screwdriver or the like and see if you can rotate it in the seat tube. It does not have to be much. If you can, its free, reach in with your tool and extract it.

The trick is the Kroil. Those of you who don't know Kroil, its about 1000x the penetrating ability of WD-40. Smells bad, but it works.