I live in Utah which is pretty arid and dry, but because I have in floor heat instead of forced air, I also see lower humidity in the summer from air-conditioning.
Using a sponge as you describe may be helpful, but I would suspect that having the printer in a less dry environment all the time even while operating is more ideal. What many don’t realize is a major part of the problem is dust and dirt in the air which can exacerbate clogs. this leads to your question, my room humidifier seems to have reduced static and dust doesn’t seem as serious. One concern with the sponge as opposed to a controlled humidity environment is mold, something to watch closely (also a problem with humidifiers so changing the wick and using a bacteriostat is important). Sponges don’t usually work very well because the humidity disperses so quickly, but sealing it in the tub would tend to trap it and perhaps would work.
An additional note, for me the humidity has been beneficial to roll paper such as gold fiber and exhibition fiber, so the benefits are more than reduced clogs. I think it helps even sheet papers.
Many clogs in epson printers may result from something other than dried ink. I think as the printer sits, the pressure drops and allows air to enter the nozzles. Certainly this can dry the ink and create an issue, but until that air is purged no ink comes out either. End result is the same, it takes cleaning cycles to resolve, so really probably doesn’t matter which is the cause, other than perhaps this type of missing nozzle tends to resolve easier.
