Does anyone else in the family speak loudly or is it just her ? Could she be trying to make herself heard above other clamour?
Mostly, is it just voice volume that you're referring to? I know you mention that she talks back and is naughty, but i get the feeling that her typical voice volume is too loud.
Have you tried video feedback? She probably really doesn't know how loud her voice is. To use video feedback, you tell her ahead of time, in a positive and cheerful way that her voice is loud and you're worried that over time she'll damage her voice and throat, so you want to help her speak at a normal volume. Also, other children will be more likely to want to sit near her if her voice isn't so loud.
And then just set the camera up and go about playing in the pool or having dinner, or whatever you do. Later, together, play it back and let HER comment. What do you think about your voice? Does it sound louder than everyone, or about as loud as everyone else? Hmmm. Can you talk more quietly? Then get out the video camera again and encourage her to use her new voice, and video tape her talking, showing off her toys, whatever, in her new voice. And then show her the video, does that sound more quiet?
This can be really fun for her if you let it be. Video is so profound - often people have no idea what they look and sound like until they see it.
Best wishes. The trick here is to keep it positive, and fun, and not punishing or shaming.