He does have a humidity box exactly as you described (sizable lidded tupperware with a hole cut out and damp sphagnum moss within) and he's been using it quite liberally.
As for keeping the humidity up I've resorted to literally just sprinkling entire cups of warm water throughout the enclosure whenever the readings dip into the 60's. The substrate is a coconut fiber and sphagnum moss mix so I'm no worried about mold and rot but I plan to completely clean everything out after his shed is done anyway.
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Sounds great! Please post an update after the shed and keep up the great work.