Do you know if using the DMZ feature on most routers instead of port forwarding would get around this limit, or if there's any other way?
It's done via /etc/sysctl.conf
> net.netfilter.nf_conntrack_max=32768
Afterwards "sysctl -p" to apply/ reload the config file. But increasing blindly is a bad idea… it needs to be done with ip_conntrack_buckets in sync for proper balance (memory use, CPU usage). Best to read upon it.
But just going from 16K to 32K shouldn't be any problem for most routers these days.