First thing you really MUST do, no question about it, is stop eating rice cakes! they are not healthy - puffed cereals are poison proteins - and very dry, they definitely create dry, compact stools. I use sliced Jicima, a nice crispy vegetable, as my cracker when I need one. :) It goes great with nut butters.
You're drinking enough water to not be dehydrated. Having constant dry mouth and such, constant thirst, is usually a weak pancreas, and the adrenals are sometimes involved because the pancreas and adrenals "talk" to each other. I seem to recall you were tested for diabetes and it came up negative, is that correct? If not, do see about getting that checked.
Definitely increase your intake of good oils. Use homemade oil/vinegar salad dressings liberally. Go for pasta every now and again and swim it in olive oil, butter, garlic and basil. Yum!
The slower your stool transit time is, the more chance that the colon will absorb the fluids in the stool. The cure is eating foods that have a faster transit time, and/or include both soluble and insoluble fiber that tend to retain water. Most fruit and veggies fit this protocol, some grains, and preparing them with pungent herbs/spices helps too.