Now that MIG welding and silver-soldering have been abandoned I have to decide on Plan C, and I suspect the dreaded pop-rivets may feature prominently in it. It's likely though that I will put the heater project on the back burner for the time being and concentrate on the things I need to do to get Fenchurch through her MOT test instead - I want to get that over with before the end of this month if possible, so spending another week on the heater now would probably be unwise.
On a more positive note, here's a picture of me and Fenchurch. That weird facial expression which you probably recognise from my default userpic is me trying to fake a smile for the camera and failing badly at it.
Update: I've taken today off work, so I decided to have one last try at silver-soldering. I managed to get the ratio of water to flux powder better than I did previously and the flux paste went on quite nicely. I rearranged things so neither side of the joint was touching the (highly heat-absorbent) firebricks of my makeshift hearth. I quickly heated it up to brazing temperature, and the middle of the joint bowed way out due to insufficient clamping. I soldered the ends of the joint, then let it cool down hoping the bow would go away when it cooled down and the metal contracted, but it didn't. I rearranged the clamps to press the middle down and reheated it. The middle of the joint didn't stick (presumably the flux was exhausted by the first heating), and the outer ends came partially unstuck, leaving a joint that is poorly stuck together at the ends and has a huge gap in the middle. Doh :( I suspect the proper way to clamp a joint like this for brazing may involve fitting temporary screws or steel rivets along the length of it, then cutting them off and filling in the holes afterwards. I can't be bothered with that, so I officially give up on silver soldering. I have a tentative Plan C forming which involves using a thicker gauge of steel that doesn't instantly burn through and distort when I try to MIG weld it.