I don't have personal experience with dice storage, but based on the guide lines in the article, using a prescription bottle without a cap might be best. If you want to keep dust out, you might cover the top with an open-weave fabric. I'm not sure just a hole would be sufficient to vent the acid gasses.

I thought the recommendation in the article to store film in a freezer was interesting. Not really practical if you want to display your plastic items but gives you an idea of what is the best environment in the extreme. Avoiding temperature fluctuations was another recommendation. This suggests that keeping them in an air-conditioned and heated room was advisable, and probably avoiding direct sunlight as well.

There have been collector articles written that suggested coating the dice with clear nail polish. That might be a solution if your dice are already crumbling; it would at least keep the pieces from falling off. I doubt it would address the real problem of decomposition of the cellulose acetate though.