I'll give a summary to get back on track:
1. There is data that says that the speed of light decreased.
2. There is data that says that the earths rotation is not constant and even slowing down over at least the last 30 years.
2 can provide an explenation for 1.
If we just look at the data and not the theories first, we see that the earth spinned faster in the past. This implies that the orbital second used in the past to measure the speed of light with, was shorter. This explains why the speed of light was measured higher in the past.