By trading. With sentient goods it works the same way as with the normal goods: you build only your boosted sentient manufactory and trade for the other two.
- In your planks manufactories you continue producing your boosted planks. You trade for marble and steel. (You don't produce tree gum in your planks manufactory, because it's horribly inefficient.)
- In your marble manufactory/ies you produce boosted moonstone. You trade for tree gum and platinum. (You don't produce marble in your marble manufactory, because it's horribly inefficient.) Also you need to have 500 marble relics to have the maximal boost bonus (just like you have 500 planks relics to have the maximal planks production boost.)
I've got one remark to your setup: it's enough to build only one sentient manufactory, if you keep boosting its production with Magical Manufactoring spell. For me personally it worked with one sentient manufactory of each tier (T4, T5, T6) up to and including Constructs chapter. Elvenar then are another story, but you don't need to think about it now. ;-)