The problem of having very high humidity in the ambient air is making the ac work extremely hard in your house, thus not cooling as well as it should. Your ac works to cool, but the energy it uses to remove humidity is a big problem.
As far as ice packs, I dont think that having them inside is a problem as long as you have something under the ice pack to catch the condensing water off the packs. Those ice packs will sweat like a mother! They should not pull too much humidity though as they are just a passive cooler. If you have a fan blowing air around inside, then I would be worried that your humidity would drop to an unacceptable level. Now I have never had this problem, so maybe some of the other posts above might be helpful, just a little food for thought from your neighborhood refrigeration and ac specialist :]