Ugh, that's the worst. Those fancy pots are such a gamble. My basil never stood a chance with one. Now I just use a cheap plastic bottle with a hole in the cap. Works way better than anything I've bought.
Check out the brand Blumat, their little clay cone things actually work. Learned the hard way like you with a fancy pot that drowned my herbs. Now I just use those cones in regular pots and they keep things perfectly damp.