I just remembered a PACE solder rework station that we had at one of my previous places of employment. We had it as we used to do board level repairs on most of our electronic kit.
The interesting thing was the hot air soldering tool that was intended for use with surface mount components (station included a 20x stereoscopic microscope, it was a cool toy). So anyway the point is that the soldering was done by painting solder 'paste' on the target region placing the component and then hitting with the hot air gun. The paste would turn into little balls of molten solder and when the temperature was right would form a very nice joint.
I am thinking that this may be a technique that would work with the heavier copper particularly if it was preheated. The problem with traditional soldering is that the heat is dragged very quickly out of a soldering iron tip, you basically need to use a very large tip if you are working on objects this size.
Soldering is quite an art, we endured considerable training to learn proper technique.....which I have not used for 10 years so probably lost most of the skill