Well this is embarrassing - the high (320ppm) reading I measured may have been the result of instrumentation error.
I've continued taking readings on the RO water stored in the kettle. I have been able to reproduce the high reading with a measurement 30 minutes ago of 380ppm, but I'm also getting some readings in the 5-10ppm range, which is what I would expect from RO water.
My procedure is to clean the instrument with distilled water, rinse the sensor and sample cup with the water to be measured, take a sample, agitate the sample, and take a reading, allowing 10-20 seconds for the meter to stabilize. This is how I arrived at 320ppm, which I was able to repeat with a second measurement. However, today after I measured 380ppm, I measured some tap water (60ppm) and went back to the RO water, at which point my meter read 8ppm. I repeated the measurement of the RO water, and was still in the 5-10ppm range.
At this point I think it's more likely the RO water in my kettle is sitting around 5-10ppm, and the 300+ ppm readings I have measured are the result of some instrumentation error. Strangely, I get consistent results from tap water and RO water stored in glass jugs. The RO water stored in the kettle seems to throw a high reading at times. I'll try re-calibrating my meter and continue testing.