Bazyle,
as you surmise, the grids pile on each other, supported around the perimeter. I cut the middles out of a couple of the grids to give space for the filament roll.
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Regarding PLA, I find the behaviour perplexing. If I leave the filament in the printer for a few days, I find that only the first 6 inches of the roll becomes brittle. The rest seems to be fine. It’s as if the moisture is absorbed up the length of the filament, which I find hard to believe.
Rod