I think your "preamble" is not "really necessary", as you state, to give my response context.
My assertions stand on their own, balanced is not a sonic guarantee of anything. Neither is it a detriment. Maybe it will be quieter in your system.
As for noise, not all is cancelled out. We often will see a circuit with additional parts. Not perfection! I have no horse in the race but I don't like "black and white" statements, high end audio is too full of them, and most of them are wrong. And if you have ground loops, balanced dies not kill those.
To get back to your original question, "My question is whether the balanced option should tilt me in favor of one type vs. another", don't let this one feature tilt your decision. I never heard it be the make or break for any phono stage, and I have tested a lot of them, including many of those reviewed as the best, and own a lot of them.
Listen to everything you can get your hands on, don't pre-judge or limit your field based on things like balanced or not, use of signal transformers or not, specifications, circuit design features claimed by the manufacturer, or reviews. Go to lots of concerts without PA systems, listen to solo instruments whenever you can, and try to match that feel.
Again, no connection to retail sales or electronics of any type. Just a guy who hates the hype in this industry. It's about the music. Don't get lost in the technical claims.