If you use DHCP, then I think you can configure that. What I have in mind is to assign static IPs to all of my fixed machines anyway, and use DHCP to assign IPs to transient machines. Not sure if that's reasonable, but it's my current thinking.

> does every router (even crappy ones) respect the no-forward rule?

There may be broken ones, but it doesn't matter so much because your ISP won't route such addresses regardless.

If a connection comes into your router with the destination IP set to one of your LAN machines, NAT will not stop the connection.

There's no reason to be using NAT to protect yourself from inbound connections, because that's not a thing NAT even does in the first place. It often makes things actively worse even, by making it easier to port scan for your servers and by giving you a false sense of security.

They are called Unique Local Addresses (ULA) and are in the range fd00::/8.

Which itself is so much better than RFC 1918 addresses. If you need private, non-Internet routable addresses, then you generate a random one. In the event two private networks need to communicate over VPN, for example, there is no clash.