The air humidity isn't as important if the soil is wet enough (still important, but I know some climates really make that hard). Don't make it swampy or anything, but maybe make the substrate a bit more moist. That way the frog's skin will stay more hydrated, and also the humidity at the level he's breathing will be closer to what it should be.

Also, how do you have the top of the tank? If you don't already, you can tape saran wrap (cling wrap) over about 2/3 of the top. That also holds in humidity and keeps it more constant.