iOS app won't connect *inside* home network

I just set this up and it was remarkably simple even without the access to add-ons

Just for fun, in case anyone runs into this issue again: it looks like a recent firmware update to some Asus routers has added a feature that can cause this problem to reoccur. The firmware update adds a new option under the WAN configuration called “Forward local domain queries to upstream DNS” and it is turned off by default. If you update your firmware and the connection issue described here occurs, you may need to turn this option on.