I think you're doing great - exactly what we did. She will stop, eventually. I know with my DD, she was looking for a reaction more than anything. We tried to keep it as low key as possible, never giving her much of a reaction - just saying "gentle touches" and taking her hand and demonstrating that. You could also try "hey, give mama high 5" whenever she hits. That way, you're modeling an OK way to hit, sort of... When she's not in the sling, how about offering a drum or a ball to hit.
I know others will have better advice, but don't worry, she won't be in this stage for long. Hang in there!
I know others will have better advice, but don't worry, she won't be in this stage for long. Hang in there!