I'm not balanced enough in order to do a squat at shoulder width, so I do it a bit wider (maybe another 6 inches wider or so). I feel my gluts, hams and abductor being worked considerably. Should I try and learn a narrower stance to hit the quads more?
for now no because you said you aren't "balanced enough."
so just keep trying with lighter weights, and deadlift(with standard stance) , that might help you with balance.
You can also try front squats.
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a shoulder width stace is actually quite narrow. It sounds like you are right where you should be. If you really want to squat narrow try putting something under your heels, like a 2.5 lbs plate.