Lets see.

Run towards them (predator) vs run away (prey) - got that one right.
Make Noise (predator) - got that one right
Defending vs Attacking - no real right answer, no one got hurt so you did good.
Extending your reach with 5' of hickory - real good answer.

As long as the dogs were held a bay, shooting would probably be considered excessive. If the dogs had attacked someone, you should use the stick (or your feet) to beat them away from the person and then consider escalating to firearms.

Sounds like everything worked out and I don't see how to improve on the results.

Congrats on a good response in a tricky situation that doesn't allow much time to think.

- Eric