I had a Quarter pony mare once who CONSTANTLY lipped/mouthed/chewed/chomped anything in or near her mouth. What I mean by "near" her mouth is she has been ridden in also a hackamore and she would reach sideways with her lips and try to grab the shank to pull it into her mouth. When she did have a bit, whether a simple broken snaffle, to a broken curb she was always chewing, mouthing, or moving it around in her mouth. There was nothing wrong with her teeth, she just had the habit of messing with the bits and if it wasn't in her mouth she'd grab it to put it there. It was rather amusing.

You don't mention how long you have had her. Is this something that she has done all along or is it getting worse. Is the snaffle-a snaffle is any bit that does not have leverage,regardless of mouth piece design/joints- the exact same as what she was being ridden in before. When you look at the bit the corners of her mouth should look like shes "smileing" but not so tight as if she was "laughing" apprx. 2 wrinkles. When the bit is in her mouth holding both sides you should only have apprx 1/4 inch past her skin. The metal, if the part that goes into her mouth is made up of a copper or composite it tastes just like a penny and is used to encourage salivation and mild chewing. She is still very young @ 4, sometimes bit chewing is not mouth related but due to fear/confusion/uncertainty or pain those are other possibilities to look into.
I get my horses teeth done 2x year spring and fall by a licensed equine dentist, they are not licensed vets so can't give medications/sedations have used the same guy for 11 years as to date have only needed to sedate 1. Also use the traditional hand done method, believe that anything mechanical doesn't need to be in my horses mouths. Your dentist should be half the price of your vet. We have domesticated and changed the diets of horses to such a drastic degree that they aren't given the opportunty to eat the stuff that would naturally keep their teeth in good working order.