Some thoughts:
...3" of drop, while not extreme, is still probably contributing to the problem. But with a threadless headset there's not a lot you're going to be able to do about it without a fair amount of work and expense. If you can get your hands on a stem with more rise, it would be worth experimenting with. (The next step after that is replacing the fork and cutting the steerer taller.)
...A bit less stem extension can also serve to move you to a slightly more upright position.
...Have you tried looser shorts? Seriously. Analyze exactly where the pressure is coming from and you might conceivably find that some or all of it can be relieved by giving the scrotum someplace to move so as not to be squeezed by the saddle.
...Sometimes when riders have trouble with level saddles, it's another indication that the reach to the bars is wrong (too long, usually), as well as that there's too much drop. The too-long reach tends to pull the rider onto the nose of the saddle. The feeling of sliding forward can have the same cause.
...A too-wide saddle can sometimes cause the rider to sit too far forward.
In general, I'd suggest that you revisit your basic bike fit. The most important part of bike fit is simply achieving comfort, and yours obviously fails in that regard. The amount of drop to the bars is one aspect of this, and if 3 inches of drop is causing the discomfort, maladjusting other parts of the bike is not the solution.
Many non-racers, particularly tourists and commuters who put in a lot of miles, set up their road bikes with zero drop. It's not racy and stylish, but neither is testicular pain.
RichC