I did get a look at, at least a summary paper for the GRAAL experiment.
A NEW LIMIT ON THE LIGHT SPEED ISOTROPY FROM THE GRAAL EXPERIMENT AT ESRF, (2010) The actual data for the experiment apears to be spread out over several papers, referenced by this paper. I have not looked at any of that data.
THIS IS NOT AN IN DEPTH ANALYSIS OF THIS PAPER. THAT WOULD REQUIRE SOMEONE WITH A GREAT DEAL MORE EXPERIENCE AND KNOWLEDGE OF THE METHODS, MECHANISMS AND PARTICLE PHYSICS, THAN I... And probably more time than I spent reading through the paper. With that caveat, my impressions are as follows...
The experiment does not measure the one-way speed of light. (Tach never claimed that.) It compares the one-way speed of photons, over time and direction and does not find the comparrison to be isotropic. The experimental data as interpreted, represents a null result, as it was intended as a test of SR which assumes that the one-way speed of light is isotropic and the experiment does include Lorentz transformations (another component of SR).
Even though they are working with a one-way light experiment, I would place this in the same catagory as a M&M class of experiment, where the speed of light over different paths is being compared. One-way speed in this case... The paths in this experiment being subject to the Earth's motion, including rotation, orbit ect.., all ultimately assuming the CMB, as a frame dependent isotropic background. This paper notes an anistrophy in one-way speed of light over the course of the experiment, but makes no assertion as to the cause... And does note that further study is required, followed by, "
... clearly shows that there is no evidence of the 24 hours cycle that one would expect from the rotation of the Earth." Saying in essence, they did not get the results they expected, while they did so with better precission than earlier tests.
I did not spend a great deal of time on this paper and did not look deeper into the data it refers to in the additional papers. That said from what I see here, after accounting for the expected Lorentz transformations, which should have returned a variation in the one-way speed of light relative to the 24 hour rotation of the earth, they found no associated variation, their results were isotropic after Lorentz transforms were accounted for, and thus the experiment returns a null result. (Keep in mind that the Lorentz transforms, applied after the fact , were an explanation for the null results of the two-way M&M class experiments.) Transforms applied in advance of data analysis in this case should have returned a variation...
Since this experiment was fixed relative to the earth and all rotation was relative to the Earth's motion, compared to the CMB preferred frame, they were not comparring the velocity of light between the two legs of a two-way light path... So the results have limited application to the relationship between OWLS and TWLS, other than the experiments comparing the two, relative to direction of propagation both return similar results. This should be expected. If the results had been different than the two-way experiments, that would have been big news. As it stands they appear to be consistent with the two-way experimental results, with the exception of variations in the accuracy of isotropic or anisotropic limits, depending on the experimental design.
It would be interesting to see the results of this type of experiment where two accelerators operating in opposite directions were run at the same time. That would come close to a comparrison of two legs of a two-way light path.
One further note, the only reference in this paper to an absolute frame is in the introduction or abstract statement. In the paper itself the CMB frame is referred to as an isotropic rest frame (for the experiment). The authors do not apear to me to be declaring the CMB to represent any universal or absolute rest frame.