The frequencies of three separate Cs fountain clocks and one Rb fountain clock have been compared to various hydrogen masers to search for periodic changes correlated with the changing solar gravitational potential at the Earth and boost with respect to the cosmic microwave background rest frame. The data sets span over more than 8 yr. The main sources of long-term noise in such experiments are the offsets and linear drifts associated with the various H-masers. The drift can vary from nearly immeasurable to as high as 1.3×10-15 per day. To circumvent these effects, we apply a numerical derivative to the data, which significantly reduces the standard error when searching for periodic signals. We determine a standard error for the putative local position invariance coefficient with respect to gravity for a Cs-fountain H-maser comparison of |βH-βCs|≤4. 8×10-6 and |βH-βRb|≤10 -5 for a Rb-Fountain H-maser comparison. From the same data, the putative boost local position invariance coefficients were measured to a precision of up to parts in 1011 with respect to the cosmic microwave background rest frame. By combining these boost invariance experiments to a cryogenic sapphire oscillator vs H-maser comparison, independent limits on all nine coefficients of the boost-violation vector with respect to fundamental constant invariance, Bα, Be, and Bq (fine structure constant, electron mass, and quark mass, respectively), were determined to a precision of parts up to 1010. © 2013 American Physical Society.