I biab with full volume and use a pump to recirculate throughout the mash, never had any tannic flavor and I use a very fine crush. In my mind, introducing fresh, 1.000 gravity sparge water to a bed of grain already depleted of most of its sugars is setting up perfect conditions for extraction of unwanted compounds, including tannins. I'm not a chemist, but mashing with full volume means that as extraction progresses, the gravity of the wort steadily increases until the extraction "pressure" it puts on the grain bed is practically zero. To leave the bad stuff behind, get yourself a Wilser bag, mash full volume, and don't look back. Oh, and resist the urge to squeeze the bag, just let it hang over the kettle.