I dig some more digging and it gets a bit more interesting. When I am unable to get to the web admin page directly by IP - I also cannot ping the IP of the non-wired AP.
However, when I log into the non-wired AP through the controller, I can use the PING feature in the system menu and send some pings out to the LAN. After those packets go across, I can ping the AP and access the web admin site.
It looks like there may be an issue with ARP or routing whenever the AP is attached via mesh. Any thoughts?