Sounds good - let us know what happens Monday. Remember, those UBNT ToughSwitches are 24V only, aka UBNT-proprietary - they will not work with standard 802.11at/af cameras. Additionally, I'm not sure if the QSee unit is proprietary or standard-derived either. So may be better not to introduce foreign elements - stick with what QSee gives you in their boxed-solutions, at least while troubleshooting.
Long shot - did QSee supply ready-made cables in the packaging? If so, try those, in case the pinouts are proprietary.