At this point in the project I *could* design and order a PCB for debugging and development, but not yet.

I'd rather start with some bodge wiring and see where that leads. The wiring map (developed by Connor Huffine) might have some bugs, the LED panel might turn out to be damaged (or complete crap) and I really want to see if I can weld the bodge wires.

Bodge soldering 0.05" header pins is tricky and a PITA, so I've been meaning to try welding instead.

Question first: will this work?

With a great deal of fiddling, I managed to get a wire and the header pin between the two electrodes of my battery tab welder and tried welding.

Answer: yes!

Surprisingly, this appears to work very well. The wire ended up weld-bonded to the header pin, and pulling the wire with reasonable force (force close to the yield strength of the wire) does not make the weld come loose. 

The official test of a spot weld is when you pull two pieces apart: if the spot weld is any good, the material will fail before the spot weld and you'll end up pulling out a section of the material instead of breaking the weld.

...and that's exactly what happened!

A sufficiently convenient jig that holds the wire against the header pin between two electrodes should work, then I can apply a line of hot-glue to the welded wires/pins to act as strain relief.