I lf i were doing this, I would be paranoid that it would dye unevenly, or get too dark while I was trying to get it even. I think I'd cut it into the smallest pieces possible. Then i think instead of tea dying, I'd do it with instant coffee. Easier to replicate the results. Or do a really big batch of really strong tea to use as the dye, diluting it according to a recipe determined by experimenting on those fat q's or 8ths. But before that, I'd call Dharma and ask if they have any advice. You might also thinl abput using gray or black instead of brown, if a cooler rather than warmer color would go better with the colors you are using. But you've probably already considered that, as vlever as you are.
It's a little daunting giving advice to some of you. I feel myself getting out on the limb, and it's getting a little "whippy." I sometimes wonder if the first thing the OP thinks after reading my answer is, well duh, but I wouldn't want to skip that one thing that ends up being important. XXOO Patti