How to filter a LVDS clock properly
Probably what is happening is there is intra-pair skew between the clock line pair lines. Any imbalance in the pair has to make its way back via ground or any of the other connected signals as common-mode noise. This is true of the other pairs as well.
A common-mode filter on the clock will definitely help (as it will with the other signals too.) There’s a whole product category of 0402-sized CM filters designed for HDMI that can be used for this.
Could also try an overall ferrite clamp-on filter for the cable.