Indeed your explanation made us find each other in a more understanding position. Lol
As per the UPS is concerned, Sadly you cannot put it to use any more except for lending it to some guy on rent or donating it to your poor friends.
I'll explain the reason with an example to keep it simple, It's like installing a CNG kit into a Prius.
I can come up with a stupid system design to design a backup for your UPS (which already is acting as a backup) to be a backup to your backup.
Although I have a good news. We can do something with the batteries.
For that I would want to know the Specs (Ah, Voltagr) of your Dry and the other battery.