Re: Seat post stuck
I think if aside of all the ideas and of course also getting a mill and jigging it up to take out just the post, maybe leaving it in. What I mean is using it in some way to clamp something that post sticking out. Then laterally forward or aft have a metal connection that has another seat post that can move a small amount up or down. Kind of analogous to those lay back seat post setups.
It may not be what you want or have room to work, but maybe?
If cutting out the frame portion and welding back in a new section can be done by you or economically some how, throwing out the frame would not be necessary. I've welded a bit, but not brazed or used a torch. My MIG has some limitations.