@Ironhorse: I used to do that too, but once someone tips it over... frustration.
Prior to me abandoning my childhood
, I was using plastic utility boxes. (Sewing, fishing, tool box, whatever had the right size slots) Same divider idea, but you can close the lid so the fear of something tipping it over (like a child or cat or stacking trays/boxes) and having to sort and re-separate pieces is reduced greatly. I know it's pricier, but saving yourself from even a single session of sorting a mixed batch of Lego IMO is worth it. I could typically find them for around $5-15 bucks or so and never really needed more than 1 or 2.
Although if you can find a plastic box with a lid that neatly fits the cutlery tray, you could probably stack those trays inside and emulate the plastic utility box idea.