Thanks for all the great advice.
The tip is screwed on very tight. I've been holding it to the metal to be soldered for a good minute and it won't melt the solder, not even if it is about 1mm away from the tip.
I don't know what a good liquid flux would be. I just went to Lowe's and picked up the only silver solder they had, the Bernzomatic I mentioned earlier. It has a white paste-like flux with it that you put on with a little brush. Where would I get the flux and silver solder that I've seen mentioned here, preferably locally? Lowe's obviously doesn't have it, and I don't think Sears does either.
Since the torque rods are not being assembled near the model would I just be better off using a small torch? I haven't been able to find a soldering station anywhere locally.
This is irritating as I can't do too much else to the model until I get this part put together.