As you have logically suggested since the AYC oil is for the clutch packs then I would have thought a LSD oil would also do.
I would only suggest you use LSD oil as a last resort if you definitely cannot get hold of AYC oil.
Whatever u do, do not try and substitute the AYC oil.
The AYC fluid appears to be a combination of ATF and diff oil, but only they have the recipe.
We need to get it analysed by gas chromatography or some sh!t like that.
U must try and get the original item from Coordsport.
The Original stuff works, I have covered over 59,000 miles in my E6 gsr and its only £11-12 a bottle ( 1 litre)
and u only need 0.7 l for the AYC fluid change.