Differential amplifier noise

Your breadboard has lots of antennas, which is not helping with your noise problem. Twist the two wires going into in+ and in- together and see if that affects your noise level. If those wires are closely coupled, the effect is that the coupled noise is equal on both wires and will cancel at the +/- inputs of the differential amplifier. If that helps then maybe you can figure out a way to mount your amplifier on your load cell and shorten up/twist the wiring to good effect.

Not sure what to suggest about the one separate gauge. I can't tell how it is wired or whether or not the cable is shielded.