I'm no expert, but it looks like the left pin is what connects to the diodes in every row except for the row with shift, and each of the traces connected to the diodes run out to the rest of that row, so whichever legs aren't connected to the nearby diodes should be part of that column. The caps lock vias look totally destroyed, which probably broke continuity between caps lock and the rest of the column. Caps lock just appears to just so happen to also be the point at which that row runs back to the controller.
Assuming all I can tell from those somewhat blurry pictures is correct, you should only need to reconnect the column at the break by bridging the following pins with 1 or 2 jumper wires:
If I'm reading what you said right, I think that aligns with what you've said about bridging pins to test their outputs as well.
It looks like shift has alternative vias as well, so with that key you could just solder to the unused via if there's continuity between it and the existing switch's pin.
It appears that this might be your first time soldering. Have you got a temperature-controlled iron and/or some flux? A lot of those solder joints look dry and may not be making good continuity. Reflowing with some flux so that they're shiny and you can tell that the solder has actually stuck to both the switch legs and the vias should help prevent some headaches in the future. Too much heat can cause the vias to lift off of the PCB, so only use as much heat as you need to melt the solder for as long as you need for it to stick well.
