But as c has decayed, the timings have changed too. If c-decays then 'ticks' have diff. Some of them are at thousands light years from us. Though not change of period of LMC-binaries may not been measured, no remarkable miraculously different period has been observed. This also indirectly refer to constancy of c.
Binaries lie in different distances.
Many of those measured trigonometrically by Hipparcos-satellite. Theirs constancy of periods and that some of them are found up to LMC all together shows constancy of speed of light.