If humidity is an issue, Home Depot sells different "Damp Rid" type products, dessicant is also a necessity for any climate except the Arizona desert.
My ammo is stored in milsurp ammo cans, with dessicant packs bought at the Army/Navy store, (we still have one), but can be bought at Cheaperthandirt, but available at many other places including Wally World.
You can keep your ammo in the wooden box, if you get some Tung Oil, and dessicant. Wipe down the box every 3 to 5 weeks inside and out, rotate your dessicant at least once a month.
Living in the Fl swamps, keeping your powder dry takes on a whole new meaning. With winter coming lower humidity helps.
Just my .02 cents