I have both a large water bowl under the lamp and a wet moss log hide. Haven't had a mite problem. And 2/3 of the lid is covered in foil. i'll try to get a pic tonight.
On the up side; he did weigh in at 99g last night, up from 82g a couple of weeks ago. so he is putting on a little bit of weight, which is good
I'll try the cup thing in addition, but he is pretty curious so he will probably knock it over. He won't allow the thermometer to stand up for more than a couple of hours without toppling it, then staring at me and daring me to stand it up again.