I have already created what you are talking about, and it works great for maintaining humidity. But you are going to need something that pushes air in the bottom of the tank to make sure the air doesn't get stale. It also pushes the moist air up into the screened portion of the enclosure.
But it was well over $100.00 dollars to make just the screened part alone so it really doesn't save that much. Unless you know a place where screen making material is cheap.
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This is how mine came out, if you consider I got two cages in one maybe I did save some money. Not sure enough for all the work unless you like this stuff like I do.