It doesn't sound completely like an imbalance problem. It sounds like you're not tight underneath the bar, and you're favoring one side coming out of the hole not necessarily because of a strength imbalance, but maybe because of a flexibility or coordination imbalance as well.
Keep doing squat, but just make sure that you're doing SOME unilateral work. You don't need a fleet of them; just try throwing in three sets of Rear Foot Elevated Split Squats into your routine on lower body days. I'm guessing that initially you won't even feel comfortable doing ten reps with your weak leg at first, but what I would suggest is that instead of basing the load on your weaker leg, base it off of your strong leg.
So let's say you can only get 7 good reps with your left leg and you can do 10 with your right. Don't just do 7 reps with either leg. Do 10 with your right, 7 with your left, and then do 5 more with your left for good measure.
Eventually the balance will work itself out if you don't just ignore it.