IPv6 doesn't have a NAT standard the way IPv4 does. There is an EXPERIMENMTAL RFC for one-to-one NAT (one outside address for each inside address) on IPv6, but explicitly forbids what you want to do (I highlighted it below):
6. A Note on Port Mapping
In addition to overwriting IP addresses when datagrams are forwarded,
NAPT44 devices overwrite the source port number in outbound traffic
and the destination port number in inbound traffic. This mechanism is
called "port mapping".
The major benefit of port mapping is that it allows multiple computers
to share a single IPv4 address. A large number of internal IPv4
addresses (typically from one of the [RFC1918] private address spaces)
can be mapped into a single external, globally routable IPv4 address,
with the local port number used to identify which internal node should
receive each inbound datagram. This address-amplification feature is
not generally foreseen as a necessity at this time.
Since port mapping requires rewriting a portion of the transport layer
header, it requires NAPT44 devices to be aware of all of the transport
protocols that they forward, thus stifling the development of new and
improved transport protocols and preventing the use of IPsec
encryption. Modifying the transport layer header is incompatible with
security mechanisms that encrypt the full IP payload and restricts the
NAPT44 to forwarding transport layers that use weak checksum
algorithms that are easily recalculated in routers.
Since there is significant detriment caused by modifying transport layer headers and very little, if any, benefit to the use of port
mapping in IPv6, NPTv6 Translators that comply with this specification
MUST NOT perform port mapping.
Also, you will find that NAT breaks some IPv6 features.
IPv6 has plenty of addresses so that you do not need to use NAPT the way you do with IPv4. NAPT on IPv4 breaks the IP paradigm where each host is assigned a unique address so that connections are from end-to-end, with no middle devices needing to maintain state on the connections. IPv6 restores the IP paradigm, allowing protocols other than TCP, UDP and ICMP*, and it fixes applications and application-layer protocols that are broken by NAPT.
You may misunderstand the tracking and function of Privacy Extensions. The fact is that the tracking that Privacy Extensions prevents is tracking a device as it is connected to different networks, getting a new address on each connected network, not tracking the services that the device uses on the Internet. By using only the original SLAAC, a device will always have the same IID (Interface Identifier) on the same interface, and it could be correlated, no matter the network to which the device was attached, tracking it as you move it from network to network. This does not matter if the device only exists on a single network, you have no movement to track. If you do move the device to other networks, and the device does not support Privacy Extensions, then you will be able to be tracked, but I would also argue that the device software is so old as to be riddled with security problems.
If the device only connects to a single network, then there is no tracking risk, and you could also use DHCPv6 to assign addressing, or you could manually assign an address, rather than use SLAAC that uses an identifier, such as a MAC address.
*RFC 3022, Traditional IP Network Address Translator (Traditional NAT) explains IPv4 NAT, including NAPT in Section 2.2:
Sessions other than TCP, UDP and ICMP query type are simply not
permitted from local nodes, serviced by a NAPT router.