Updating here, I had some more time today to play around with this. Installing resolvconf seems to have solved my problems.
sudo apt install resolvconf
This article helped me figure it out, https://www.ricmedia.com/set-permanent-dns-nameservers-ubuntu-debian-resolv-conf/, I had already done the configuration and only needed that install, but if you came here looking to set permanent static DNS servers it looks like it should help you out as well.
