They must be getting stock soon given their logo is on the LP set that's in the wild already.
I don't think it's a matter of which company is releasing which edition (LRG or Justforgames). But more about the type of wax each edition uses.
I suppose the exclusive translucent edition could be produced faster than the gold and silver one.
On their website, Justforgames did announce a September 3rd release date for their exclusive Glow edition, which proved to be true. And they add that the Collectors edition will release on October 15th.
So maybe general distribution will get the other vinyls on September 24th as Amazon said... Or it will be delayed to October 15th...
We will see...
Source in french : https://www.justforgames.com/fr/produit/shenmue-iii-original-soundtrack/