Hi John,
Yes it can definitely help to have a better controlled environment for fruiting in…we realise this is something in the current course material which is slightly lacking, so are soon to update it with an instructional on how to make something like this:

It’s just a 3 tier greenhouse with 6 x 3cm holes cut on each side of the plastic, and a mini pond fogger placed in a tub of water in the bottom. When the front is zipped down it creates the ideal balance of air exchange and humidity and can be left alone for a few days at a time without care.
You could create something on a smaller scale like what you already have in your plastic storage boxes, by just drilling some air holes in the side and then putting some wet perlite on the bottom of the container for the humidity.
Hope this helps.
Best wishes,
Adam