Add more hard oils and less soft oils in your recipe. Add sodium lactate or vinegar to the lye water. If using vinegar, you have to do some calculations or use a
lye calculator that does the maths for you, like
soapmakingfriend.com.
Also don't use a too high percent of superfatting.
I don't know your recipe, how much soft and hard oils you use, which oils and your level of superfat. But keep in mind that if your lye is not very pure (for example have become lumpy from soaking moisture from the air), then your superfat will be even higher than you think it is. The same if you add acids without adding extra lye. Tomato juice, for example. Or add extra fat but not include it. For example coconut cream.
If you have many oils, butters and fats to choose from where you live, it might be possible to replace one or two oils in your recipe with something that has a higher percentage of stearic acid. If not, you can add some in the form of soy wax, for example. Pure stearic acid can be almost impossible to soap with in cold process, depending on how much you add.
And yes, use a good soap dish. I have a very, very good one, one that is not a soap dish at all, but anyway as perfect as it can be! It is a refill for an old style dishwashing brush, turned upside-down. When it gets dirty with soap, just wet it and wash the sink with it, then rinse and shake and it is good as new. Looks stylish too, plus very space saving. It is one of these (just turn it upside down and place te soap on the brushes. The soap will not slide off):