It sounds like there may be a short somewhere. If you have a multimeter (or can get one temporarily from your local home improvement store), I would disconnect Yellow and Green cables from your Rachio and test impedance (Ohms) between them, it should be relatively large (10+) and larger than from either wire to the Common (white) cable.
From the looks of it, you may have a spare cable in that bundle (I see an unused wire, wound around the outer insulation of the wire bundle). It's possibly a gray wire or perhaps a purple one.
If there is a short somewhere, you could potentially use that possibly unused cable instead of either yellow or a green one.
So you have two options, either try to get a hold of a multimeter to test if there is a short or try finding if there is an unused wire in that bundle which you can use instead of one of the affected cables.
Thanks for the photos,