I tried brazing, but that didn't work out too well. All the surroundings simply ge too hot, and the joint didn't look as neat as desired. I might give this another try later, with different materials or technique maybe, but I decided to connect everything using screw terminals.

A lot of patience later:

Some carbon fibres broke, but I think that won't hurt too much. When the other side is done I'll power it up to see how much current actually flows.