For those who are confused. It's an experiment to see if gravity is smooth or lumpy. Relatively assumes it is smooth, quantum mechanics says it is lumpy. By knowing what is happening, we can tell which is more wrong. Both seem hyper accurate in their realms, but neither allows for the existence of the other.
Effectively, 2 pendulums are put close together and left to swing. Relativity says they will slowly move into sync. Quantum mechanics says they will move together in fits and starts. By checking at the end, they can see if the syncing is lumpy or smooth. They will also have to run it a huge number of times, to pull any difference out of the noise.
Previous ideas for experiments relied on forcing 2 masses into a diffuse state, then letting them entangle with each other. Getting matter into such a state is hard however, let alone keeping it there for long enough to work. The new experiment dodges around this problem.
It's definitely not an easy experiment, it's an order of magnitude easier than the other ideas though. It might even be within the realms of current equipment.
The speed of light being isotropic has been demonstrated already and I believe I know what they mean when they say "both ways" : since all demonstrations of the speed of light are based on "round way trip" from A to B then from B to A. But, no experiments can measure a one-way trip speed.