How to Use Tea in Savory Cooking Without Bitterness

I've been cooking a lot less meat, and have been stretching to boost flavors, and one of the things I've found that can work is adding tea in the background. However, as I've moved from meat to more meat substitutes or alternative protiens (eggs or cheese instead of meat or meat-subs, for example,) I've begun to have difficulty balancing the flavors, ie I use a green and everything gets too vegetal and a bit metallic, I use a smoked black and the tannins become very apparent. Do you have any tips I can use to fix this? It's also generally when I do Asian-style noodle dishes, and I would like to branch out in ways that are not well...really obvious (making a barbecue sauce for a bean and nut "meat"loaf with a lapsang souchong base, or a mushroom sauce with an addition of a pu-erh, for example.)