Poly(vinyl alcohol) should bind tannin in water solution, resulting in brown gum-like solid. Also spray drying is very good method to extract tannin from the water solution. I recommend you the work of Antonio Pizzi, who spend almost 40 years studying tannin and other bio-sourced materials.

With the help of PVP you can precipitate

I have the opposite problem. I extract chokeberry fruits with water-ethanol solutions and tannins (probably) precipitates with anthocyanins during ethanol evaporation. For this reason I loose part of anthocyanins with precipitates.

This causes another problems - with filtration in lab, pilot and production scale.

I cannot use Sephadex - it's very troublesome in industrial scale.