On the first day, I used an oxy-acetylene torch to heat the heck out of it trying to expand the pipe enough to bust the rust and gunk loose. I'd get it nice and hot, beat on it with a small sledgehammer trying to knock the rust out, then used a punch to try to drive it off, sprayed it down good with PB Blaster, then I beat on it a little more. After doing that about four times, I'd only moved the outer pipe about 1/16". My arms were about to fall off, so I propped it up and sprayed as much oil as I could into that little gap and quit for the day.
The next day, I started trying to move the immovable once again; going through the whole process of heating, beating, and oiling this permanently stuck piece of broken junk a couple more times. And, it still refused to move.
Just as I was seriously thinking about getting out a grinder with a cutoff wheel and slicing the pipe from stem to stern to get it off (and hoping I could find a piece of pipe that was the right size pipe to replace it), I hit it hard one more time with the hammer and HOLY COW, IT FINALLY MOVED!! I'd managed to move it 1/8" which was much better than yesterday's 1/16", which meant that it was only going to take me about 100 days to get this apart instead of the 200 days I'd originally estimated.
Repositioning my punch to get a better bite, I managed to move it about 1/4" more with the next handful of hits. Maybe the immovable wasn't immovable at all. I finally had these pieces of pipe on the ropes, and I had to keep hitting them before they got a second wind and started fighting back again.
A quarter inch quickly turned into a half inch, a half inch became an inch-and-a-half, and before I knew it the pipe fell off so fast it almost smashed my toe.
After all that, a broken and twisted frame, a bunch of torn metal, and a whole lot of hammering and heat, the only thing that I could find that made these two pieces of pipe get stuck together was some old dried up grease, some dirt, and a little rust. A quick pass with a grinder, a dunk in the parts cleaner, and the pipes fit together so loosely that they practically rattled.
There's some sort of philosophical lesson to be learned here, like "when you are ready to give up on something, just hit it with a hammer a couple more times".
Now, I can start welding everything back together, and I need to decide if I want to repaint the parts that has had all the paint burned off by the torch and welding (painting it almost seems like putting lipstick on a pig at this point).