About 100 g of water is the practical minimum. A 50:50 solution -- 1/2 NaOH and 1/2 water by weight.
Here is the dry time graph updated through today. My test bars are still losing weight incrementally, but the curve has really flattened out. Interestingly, the bar with the higher original water content has stayed higher throughout the dry time and appears to be reaching equilibrium several percentage points above the other bar. I would have expected it to catch up at some point. Granted, this is one trial so no trend has been established, but I find it interesting. I think I see distinct phases in the curves, with a high rate of loss in the first 3 weeks, then a secondary phase from 3-14 weeks. At about 100 days the rate flattens again with much slower changes from then on.
A soap made with "brittle" fats -- coconut oil or palm kernel oil -- will be relatively hard ... but it will also be very soluble.
A soap made with soft liquid oils -- monounsaturated oils (olive, almond) or polyunsaturated oils (safflower, sunflower, corn, etc.) -- will not typically be a hard soap, but it will be a less soluble soap.
If you leave any lye soap in a puddle of water in the soap dish, the soap will get mushy. Soaps made with mostly lard, tallow, or palm will get mushy somewhat slower than soaps made with mostly CO or PKO (hard but more soluble) or soaps made with monounsaturated or polyunsaturated oils (soft but less soluble).