How do I wire a gcfi outlet in this situation?
If you can't use the interesting bundle of wires you found, there might be another approach. Assuming the 12-2 romex came from the disposal switch (probably above the counter) you might bypass the existing switch and make the current wire to the disposal unswitched. Then you can add a switch and receptacle in the cabinet (assuming it can be made easily accessible under the sink) for the disposal and a second one for the dishwasher.

btw - my house was built in 2004 and we had to install a switch for the dishwasher as well to cut power for maintenance. If you dishwasher plugs in a way it can be unplugged for servicing, then you probably don't need a switch. But if it connects directly to the circuit, you may also need a cutoff switch.

Also you would need to confirm the circuit has enough amps to service a disposal, dishwasher, and whatever else may be on it.