Thank you, all, for the great advice!
I am happy to report that I've just received the confirmation that both my parents and my family were switched to Harmony of the Seas in November 2021. The balcony cabins have already been assigned, and they are perfectly located, on the same deck, a few cabins apart, just like we wanted!
The invoice price difference is what was expected with a slight change in itinerary. Kids Sail Free was honored, even though it is not offered on that particular Harmony sailing.
I am very happy with the outcome.