If it holds the reed then max tightness is fine. EDIT see below *It does hold it but at max tightness.
I’m not quite sure what you mean by “runs up the reed.” If the reed is held properly on the top side there won’t be any side to side movement.It’s the best lig as it runs up the reed stopping the side to side.movement.
* So it seems it isn’t holding the reed properly on the top if the reed can move sideways.
Could it be the ridge on top of the metal Link is stopping the ligature from tightening properly? In which case change the ligature for one that works, or else try turning it the other way round so screw is next to the reed. (And again, try a shim if needed)

