David Schwartz's answer is excellent, but you can simplify the routing rules a bit by having just one extra table, and using your default route for the other. I have a server that's behind two NAT gateways, and I recently went through the process of recreating that scenario between a bunch of VMs. My
/etc/network/interfaces looks like this:
iface lo inet loopback
iface eth0 inet static
up ip route add table optus default via 192.168.13.10
up ip rule add from 192.168.13.213 table optus
up ip route add default via 192.168.13.11
iface eth0:0 inet static
(this is for a setup where the two ISPs are Optus and iiNet, hence the table name of 'optus')
This, plus the line in
/etc/iproute2/rt_tables creating the table, should be all you need. You'll have two IP addresses; traffic from 192.168.13.13 will go out via 192.168.13.11, and traffic from 192.168.13.213 will go out via 192.168.13.10. Configure those two gateways to do their port forwarding appropriately (192.168.13.11 forwards stuff to 192.168.13.13, and 192.168.13.10 forwards stuff to 192.168.13.213), and the rest should take care of itself.
You may need to tweak things a bit for your situation, as you're using public IPs directly, but something like this should still work. Also, it's a lot easier to do these things in
/etc/network/interfaces and then git-manage that file, rather than try to remember how you had it set up, two years later when the system has to be rebooted!