I like the idea of making a saw with a broom handle and hacksaw blade.

I've had to remove two posts by sawing them out like this. The first one was done with just a hacksaw blade and took all day. You have to make multiple cuts, then peel the sections back.

Second time I used a Sawzall, a reciprocating saw that would be used for larger size tubing. You can't cut all the way through sincy you have to be careful of the frame. You will make a slot that is higher in the middle, but you can take a cold chisel and split the seat post. Make several slots about 1" apart, then use a punch to push the section into the center of the post. Took about an hour IIRC.