Maybe one way to do it is to add all routes excluding 172.16.0.0/12 to route through VPN so we are sure everything going out is properly handled:
sudo ip route add 192.0.0.0/2 via $route_vpn_gateway
sudo ip route add 128.0.0.0/3 via $route_vpn_gateway
sudo ip route add 176.0.0.0/4 via $route_vpn_gateway
sudo ip route add 160.0.0.0/5 via $route_vpn_gateway
sudo ip route add 168.0.0.0/6 via $route_vpn_gateway
sudo ip route add 174.0.0.0/7 via $route_vpn_gateway
sudo ip route add 173.0.0.0/8 via $route_vpn_gateway
sudo ip route add 172.128.0.0/9 via $route_vpn_gateway
sudo ip route add 172.64.0.0/10 via $route_vpn_gateway
sudo ip route add 172.32.0.0/11 via $route_vpn_gateway
sudo ip route add 172.0.0.0/12 via $route_vpn_gateway
# And finally delete the default route which handle 172.16.0.0/12
sudo ip route del 128.0.0.0/1 via $route_vpn_gateway
