The provided USB2000 4000 drivers list that they support the ADC1000-USB device, but I ran into some problems. Figured I'd post my solution here on the off chance it helps someone else.
I was able to figure out the problem by rewriting a few of the provided VIs to correctly parse the data from the instrument. For reference, I've attached the modified (working) sub-VIs I'm using to view our camera. The first few pixels were being ignored by the provided VIs, and the EEPROM was being incorrectly parsed as well (it wasn't finding the wavelength calibration coefficients where it expected them on the device's ROM). Ocean Optics's Spectrasuite could read them, so I knew they were stored in there somewhere. I was able to find them, and the "Query Wavelength Calibration Coefficient" that I modified reflects their correct locations for the master/slave input ports on the device. I also had to include the modified sub-VIs in the "Ocean Optics 2000 4000.llb" file. The camera identifies itself as an ADC1000-USB, for the record.