I can't believe it took me this long to discover this thread.
I too had this problem, and I too was a 'zipper only' kinda guy when using the facilities. I recommend the following, in this order:
1) Abandon the zipper only method. It's basically impossible to keep all pressure off the johnson, even if you don't feel it. Even a tiny bit will leave some drip.
2) If that doesn't work, the 'tuck' method is a great coverup. Much better than the shirt method, because I'd rather have drip in the bottom of my boxers than my shirt.
3) Consider not wearing Khaki's.
Never tried the taint method. I'm intrigued.