Ok, this UPS specifically has 5v output so you can wire it to the +5V terminal port that Ray mentioned above.
It is 6.3 x 1.3 x 4.1 inches
Mini UPS Battery Backup for Routers,Built-in 10400mAh Rechargeable Surge Protector with POE,Output USB 5V/2A DC 5V/9V/12V 2A for Modem,Security Camera, Smartphones (Black)
For your reboot issues, I would implement a Production Freeze type policy similar to critical manufacturing systems. Since your watering is so critical, no one should make changes or reboot the controller while any program is running. No exceptions! This is a standard practice in critical industries. Even if the system can “fail safe”, why risk it?
Then, adjust your watering programs to have short (5-10 minute) maintenance windows either once or twice a day that is most convenient for you. Then you should make all controller changes and reboots during this time.
This of course doesn’t get what you want, but it does make it work with what the controller can currently do.