How can I prevent my DC-DC converters from exploding?
This datasheet says that the recommended input voltage is 30V, but doesn't specify that it should be 60V across the whole thing. It does say that it can take a +/- 30V input, however, so we assumed that was acceptable.

Right next to the line that says +/- 30 V is the maximum applied to the input pins is a line that says +/- 16 V is the maximum to be applied to the power supply pins.

Given you had a spec telling you exactly what you're allowed to apply to the power pins, there's no reason at all that another spec about what you can apply to the input pins should be relied on to predict what's allowed on the power pins.
The absolute maximum voltage to be applied to the power pins is +/- 16 V.
You applied +/- 24 V, so you shouldn't be surprised at all that your chips blew up.
Also be aware that absolute maximum ratings are damage thresholds. They don't promise normal operation or performance. You should operate the chip at the recommended operating conditions ratings if you want to be sure of the circuit performance.