Amanda, I am working on a Tsugaru style bachi now and did just that. I drilled a hole from the butt side and filled it with lead. I don’t think I would do it this way again. It is difficult to drill a long straight hole and although the balance is OK is is still back end heavy. Even with all this it will end up being light. I would suggest going in from the side like the way you see the wooden bachi an make a thin piece of wood to fit over it.
To give you an idea how much weight you need, I am again using ebony. The completed bachi would have been around 75g. This was reduced to ~67g when I drilled out the hole. The typical Tsugaru bachi is going to be ~125-150g. That’s a lot of weight and reason why they use lead.