Hey Joe and Bogdon.   I use an old closet rod. It's about 1.25 " in diameter. Others I've heard use a small diameter stair rail. They look like a C. Broomsticks are in my experience too thin and are usually very cheap soft wood (they always break). The harder the wood the better.

It could be how the stick sits on the rim. Try experimenting with cutting the groove a little deeper, etc. I use a cross piece and let the ends sit on the tub just inside the rim. It makes for a loud bass. The Tub-a-Tone folks also say they have better luck if the neck actually sits on the tub itself.

Good luck.