This is "there are no backups."
(Even if you don't anticipate a problem with your IT staff, it's just good engineering to automatically turn off the write-enable. Nobody's perfect. I've gone to the airport without my passport once. It really sux when you do that.)
Backups get pushed from devices between 1AM and 3AM each day, so the primary backup server enables it's network card at 1 and disables it at 3.
Primary backup server also has a second network card, that in turn is attached to a small subnet containing it and the secondary backup server only. The secondary backup server pulls a copy from the primary on a weekly basis in a similar manner as the primary, disabling it's network card once it has finished.
Maybe they can hit the primary if the infection takes place overnight, but the odds of getting the secondary are pretty low.
One thing you could do is get one of those mechanical lamp timer clocks from the hardware store, and have it turn the power on/off the network card on schedule.
Of course, even better would be a physical switch for incremental backups, so a disk drive works like tape - it can physically only be appended to if that switch is "off".
Come on, security professionals. None of this has any technical or cost barriers. Demand it from drive vendors. My older drives have such a switch.