Place N stationary mirrors on the corners of a polygon with equal sides such that the pulse will loop indefinitely unless it is observed by some measurement device or any other obstacle. Take a space ship which will orbit around the center of the mirrors. As you orbit, you will pass by each mirror at equal time intervals depending on on the speed of the ship.
As you just by pass by a mirror, send a pulse to the next mirror and continue the trip as the pulse starts its looping. Depending on the speed of the ship and N and relative direction of pulse and the ship, you can arrange things such that the ship and pulse will encounter at the Mth mirror where you would like to measure the time (locally) and try to detect the pulse and confirm that the pulse is really there locally in that Mth mirror. Do the experiment for different M values in both counter-clock or clock wise directions. If you fail to meet the pulse for any calculated M value (by changing the speed of ship) in any orbit direction, you would start suspecting that speed of light might not be the same for away or towards direction.
Note that the ship is actually rotating. To avoid its complication, more mirrors can be put on the sides of the polygon and M values can be arranged to correspond mirrors on one experiment side of the polygon. So only the light makes direction change.
Actually whole idea is to switch places once the pulse starts its journey.
In this setup instead of measuring speed with delta-position and delta-time, use a property of pulse which indirectly depends on its speed (momentum with presumed directions, energy with full absorption etc.). So arrange interactions in three places: Here and now; a distant place where pulse moving away will reach and interact (then you will go there to read out interaction outcome), here but at a later time after the outgoing is reflected back to here; here but at a later time after pulse is reflected three times etc. If all measurements are the same, then you are convinced that the speed of light is what I measure here or there and independent of pulse being away or towards.
Note: It seems to me that it is almost impossible, in certain situations at least, to conduct a measurement of absolute significance that is INDEPENDENT of your theory or implicit assumptions. Roughly, I am telling that sometimes part of reality that we try to independently verify would actually be unreachable and we need a priory assumptions about it.