Thanks the problem was definitely my Motorola SBG6580 "home gateway" which apparently has buggy firewall functionality, so I need to replace it. App works great, and sorry for jumping to conclusions.

No A/V or security app is present on the device at all. It's less than two weeks old and running the stock  version of Android 4.1.1 (not 4.2; sorry). Also, it's working fine today on 4G only, so I guess I need to check if my home gateway is blocking the connections for some reason via WiFi. Any unusual ports/protocols the app uses?