A good dynamic DNS provider will give you a TTL of no more than 30 seconds, and usually only 10 seconds or so, and updates are reflected immediately so the largest delay possible is the TTL. A public IP change is pretty disruptive already, so generally ~10 seconds pretty acceptable (where it isn't, you should be paying for something with a static IP). If it's the typical forced daily PPPoE reconnect, that can be scheduled at a time where disruption is minimized. Then using a better dynamic DNS provider would take care of the worst of the remainder.
There isn't an easy way to update unbound like you're wanting. Its TTLs default to an hour, so doing that would actually make it worse.