I bought a TC rod. It fell apart, leaving a segment still stuck in the barrel. Frankly I think it's fermented chinesium garbage at this point.

The rod, that is. The rifle itself is pretty nice, T/C Hawken .50 that I may use to smack Bambi this fall if I can get a tag.

So, who makes a good rod?

(And how do I get the old rod out of the barrel when the near end is 2-3" short of the muzzle?)

Is it loaded? I have a hydraulic hand pump that I would adapt to the nipple threads and push it out.
If the bore isn't sealed you will have to remove the breach plug.

Not loaded. At least I dodged that bullet. What's jammed is a cleaning patch on a jag.

The problem I think I have is that TC designed that breech plug specifically to not be removable, which brings me back to either really skinny pliers or your idea about a pump.

Make your own...

3/8" O.D. x .115 wall aluminum tubing https://www.mcmaster.com/4568T12
+
1/7" O.D. aluminum ball knob with 3/8-16" thread https://www.mcmaster.com/6940K52/
+
#10-32 tap
+
3/8"-16 thread die

Probably cost you about $50 with shipping assuming you have the tap and die.  The OD of the tubing is correct for the 3/8" thread for the knob and the ID is correct for the #10 tap.

Have you tried canned or compressed air down the nipple to free the patch and jag?

Got the rod out (uh huh huh huh). I had some hemostats and was able to get it freed in seconds. After 2-3 days of forgetting that I had the hemostats sitting out in plain sight on my desk, that is.

So, thanks for the tip about the Creedmore ramrod. Got one on order now.

But that brings me to follow-up questions:

If I treat the bore with bore butter, do i just soak a patch in it after I finish cleaning the barrel, or is there another technique?

Also, the cleaning kit came with a tube of anti-seize. Is that for the nipple or for something else?

Regards to bore butter. Yes soak the patch and it will keep the inside coated .. its really good..

Just make sure the barrel is dry.. before you run the butter thru it.

Anti-seize is used on removable breech plugs to keep them from becoming non-removable.