Basically P = V * I. Your inverter VA goes in for P. 12 is V and you get the value of I when sized for the inverter.
Schotkey (however it's spelled) has the lowest forward voltage drop. Reverse voltage should be greater than 18 V. Amperage has to gigger than your inverter VA divided by 12.
Battery isolator diodes would be a common term.
You can also size the diodes to the load on the inverter. Alternator diodes come to mind. They should be available in 30, 60, 90 amp or higher. They can be hard to mount. Some pressed and they would need a heatsink. Even the 3 phase bridge might work depending on how the anode (+) faces. The anodes would go to the UPS's and the cathodes to the big battery.
You can use an ohmmeter or diode checker to figure out the polarity. They would be less than ideal because of the voltage drop and mounting difficulty, but will illustrate proof of concept.
Basically, with the diodes, none of the UPS can charge the battery.
Audio instal places, recreational vehicle places and junk yards are possibilities.