The library does not say whether pressed sediment is usable, or what pressing does to the extract.
It does cover the step you are at. Cho's recipe says to filter the content and keep the extraction in another jar for long-term storage (Cho, Theory, p. 66). The Cho's Solutions sheet says to pour the liquid off into a container separated by herb type (Cho's Solutions, p. 9).
The recipes also reuse the garlic and ginger. Both can be rebrewed 4 to 5 times (Cho, Theory, p. 66). The sheet says to refill with brown sugar to 1/3, then to the brim with new vodka, and that the jar can be refilled 5 times (Cho's Solutions, p. 9).
