I was able to solve this by following instructions at https://unix.stackexchange.com/questions/237460/ssh-into-a-server-which-is-connected-to-a-vpn-service, to run
ip rule add table 128 from <public-ip> ip route add table 128 to <public ip subnet> dev eth0 ip route add table 128 default via <gateway>
where the information was from ifconfig
and netstat
. I did not need to do anything else special; I just connected with openconnect as normal.