I think too many people overstate what they perceive as problems and then it causes others (like you) to worry. Yes, wind direction can cause soot to collect on aft balconies. But it isn't a constant problem. Soot happens when the ship blows out the exhaust stacks and that is only done when needed which may be once a day, and at night. They certainly don't do it during peak balcony hours. And then the other question...how much time do you really expect to spend on the balcony?
I've done at least a dozen cruises with balcony cabins overlooking the stern of the ship. In all cases, we'd sometimes wake up to find a light coating of soot on the balcony furniture. Maybe twice on a 7 night cruise. We'd go to breakfast and when we returned the steward had cleaned it up.
In other words...don't worry about it and look forward to enjoying the cruise. The Solstice is a fantastic ship. Stunning.