Even in a DHCPv6 world, you could just change the prefix and all your host numbers could stay that same. Of course, the same could be true of IPv4 publics or privates of the same prefix length. But IPv4 publics inside just isn't realistic in today's world anyway.
The ISP change is definitely one situation where IPv4/NAT situation is easier than IPv6, since you don't have to renumber your inside hosts.
But it's not so bad, if you plan and do it right. If you're using auto configuration or DHCPv6, and transitioning between ISPs, you can have both ISPs connected at once during transition, and your hosts would slowly change IPs/prefixes as leases ran out, etc, and start using the new ISP with no interruption in internet connectivity. You could configure all your networking equipment ahead of time to have both old and new prefixes on its interfaces, have routing for the new pref set in parallel for both, etc. You could also do RDNS ahead of time and in parallel with the old prefix.
For servers, you'd likely do the same thing as the routers/networking equipment, adding the new IPv6s to each interface so that it has both the old and new prefixes simultaneously. That way, you could change forward DNS entries one at a time if need be, and the servers would still be reachable by both addresses during the transition, TTL timeouts of DNS entries, etc. Obviously you'd set your TTLs to very low numbers in anticipation of the transition. You'd probably have to bounce some of the servers, or services running on those servers so they listen on both IPs.
Once everything was transitioned, you could start deleting the old statically configured prefix IPs from all your equipment.
The only real bugaboos I see in doing things like this are things such as licensing based on IPs (which is dumb to begin with, but I think some products still do it), which will create re-licensing chores. And possibly other stuff such as MS Active Directory and stuff like that, which I know is very dependent on DNS. But I'm not really familiar enough with that "world" to know how painful IP changes are. Perhaps it's simple. And of course, if you use statically configured IPv6 addresses in configuration files (/etc/hosts, etc) or scripts instead of DNS names, these will all need changing too. Which is why one uses DNS names instead where possible.