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I agree with the comments above. I've tried the solder and couldn't get the case hot enough and the solder was uncontrollable. Get it tigged.
Steve

I'm going to start off with MAPP gas and the aluminum solder sticks. If that doesn't work, I'll take it to someone and get it tig welded. 

THE SOLDER IS TOO SOFT

I've heard bad things about trying to tig stuff that has the solder rod on it...I advise skipping. 

If you can't get the work base hot enough it won't stick. It melts at 700* F  but it becomes fluid so build up is impossible. In any event the surface must be clean. That's why Jeff took off so much material before welding. 
Steve