I am sure others will have better advice for you, but I have experienced the same issue. If you are using the humidifiers that typically come with a humidor, they probably are the oasis foam. This foam is very wet and therefore gives off a very wet moisture (I know...sounds weird to call moisture wet).
After doing much reading, I bought Heartfelt Relative Humidity Beads (70%). These beads are designed to absorb moisture and give off moisture to maintain a constant humidity level. The most important part, is that the beads do not feel wet, after they are activated. In fact, the moisture they give off is in a gas form, so you do not have to worry about soggy sticks.
If you are not able to get the beads, or want to stick with what you have, I would recommend rotating the sticks away from the humidifiers. Also, make sure that once they are charged, you shake any excess moisture off before placing them back in the humidor.
BTW, the website for those beads is
Heartfelt Industries, Cigar Humidor Humidity Beads, Humidors, and Quality Cigar Accessories
Hope this helps a bit.
Jim