There are several things I just am not sure about in this situation. Apple doesn't actually say it will delete iCloud data, just that if you are over your amount, you will not be able to store more. Taking them at their word (which can be risky because they are not always terrible clear in their writings) then there should be no risk at people not having a higher level subscription during the few minutes it would take to transition.
Downgrade or cancel your iCloud+ plan - Apple Support
" If your iCloud storage exceeds your new storage plan capacity, iCloud won't sync or update your information, and iCloud backups won't complete. iCloud starts syncing again and iCloud backups resume when you increase your storage capacity or delete information to make more space. "
If you do not trust what Apple says then the solution is to take out individual bridging subscriptions for one month (the minimum available). That way when you are family-less each person will still have iCloud+. Remember to cancel the subscriptions when you have made the new family because Apple will assume you each want an individual subscription and keep on charging you.
If Apple Music is involved then definitely get bridging subscriptions. The instant your Music subscription ends, all services related to the subscription vanish. That means all your playlists.
Note that with children it is different and you may be able to do this for them with careful timing. Move a child to another group using Family Sharing - Apple Support I would guess (again, "guess") what is said in that article means the transfer is seamless for children. In that case transfer the children and then have the remaining partner disband their family and join the other. They may or may not want a bridging subscription(s).