Please report back what you figure out. I'm also looking to get out of plastic. I've started collecting and testing materials. I'm looking for materials that will hold up for a bit, then be tossed in the compost and replaced. Filter floss is a tricky one. I'm not sure what's fine enough, but will also hold up.
Here are some natural or plant-based materials I've come across that could be potential filter media:
linen cloth
cellulose sponge
reusable paper towels
rough woven cotton cloth
cotton wash cloth
raw cotton
coffee filters
Linen and hemp are pretty strong. Cotton available in many forms and at low cost.
If a bunch of us experiment and share information, we can figure out workable best practices.
Best wishes.