I do think there are ways to solve that, SLAAC and DHCPv6 have a lot of options, I wouldn't be surprised if most operating systems don't honor half of them though.
The solution could be to have the router(s) send 2 different RA-packets, one with the global routablable address and default route, the other with the ULA and more specific routes for other parts of the network.
That way the host-machine thinks there are 2 routers and thus it knows what source-address to use when talking to the router and hosts on the other parts of the network.
In other news, some people say proxy servers are the solution not NAT.
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