Debugging my NAT setup
Solution 1:
The problem was that I had not enabled the IPv4 Forwarding
configuration for the kernel:
samveen@pi3:~$ cat /etc/sysctl.d/51-ipv4-forwarding.conf
# Uncomment the next line to enable packet forwarding for IPv4
net.ipv4.ip_forward=1
samveen@pi3:~$ sudo sysctl -p /etc/sysctl.d/51-ipv4-forwarding.conf
net.ipv4.ip_forward = 1
With this, everything above worked as expected.