Cannot Git Pull From Inside AWS Private Subnet

Publicly-routable IP addresses don't get rewritten when they pass through the NAT instance.

You'll need to leave the entire public Internet address space as permissible on the private subnet in the network ACLs. If the private subnet lacks an Internet gateway and its default route points to the NAT instance, public Internet addresses will only arrive indirectly via the NAT instance.

VPC network ACLs are useful to limit access between instances inside a VPC, but their stateless nature makes them cumbersome for the type of configuration you describe: it doesn't keep track of a connection that matched an allowed outbound rule to permit the corresponding inbound traffic, so you're forced to approximate by allowing ephemeral port ranges for inbound traffic.

A more flexible approach is to use a combination of VPC routing, the absence of an Internet gateway on the private subnet, and a good iptables configuration in the NAT instance to control traffic to and from publicly routable IP space, while leaving the network ACL for private subnet instances permissive-by-default with respect to publicly routable IP space. In such an environment, placement in the private subnet is sufficient to protect instances from any outside traffic the NAT instance does not pass.

yes, you must have iptables masquerading set up on the nat host.

iptables -A POSTROUTING -t nat -s (private-subnet/cidr) -j MASQUERADE

we have the same set up, you've done everything else correctly (disable source check, point private subnet to the interface of the nat instance, point public subnet to the igw).