We present a novel method for estimating variability from static observations across the entire Gaia photometry catalog. We combine these variability metrics with color and luminosity information to efficiently and uniformly search for cataclysmic variables (CVs). This reveals a surprisingly simple relationship between color-magnitude position and orbital period (Porb) for CVs which we fit with a Bayesian linear regression model. This 3-parameter “fundamental plane” helps explain the empirical scatter when compared to the previous 2-parameter studies of the semi-empirical CV donor sequence. Cutting on this relationship we identify a sample of >3,000 short-period CVs (Porb < 2 hr), for which we estimate LISA brightness using Porb inferred from Gaia observables. We predict that 6 systems will likely be coherent to LISA in the four years of mission observations, adding necessary systems to the handful of known and characterized LISA verification binaries. We present these systems, and discuss the implications of the scatter in the CV color-magnitude-Porb relationship for the CV donor-sequence.