To anyone looking for this in the future, I never did sort out why the networking wouldn't work. My solution was to create a new VLAN for my servers like I had been planning for a long time. Setting the static IPs over to the new VLAN flushed whatever issues arose and everything works fine. I had to connect directly to the servers and reboot in GUI mode and I set the IPs that way. I have to assume that if I switched the IPs back to the original VLAN, life would work again, but I'm not going to test that now that I've set things up the way they should have been done in the first place.
noja's post in No GUI after VLAN tag change [SOLVED] was marked as the answer