Soleseife is also soap made with an excess of table salt. Just because the salt is initially dissolved in water doesn't change the chemistry.
You'll have the same problem with tallow soleseife soap (made with table-salt brine) as you would with tallow salt bars (made with solid salt).
The lauric and myristic fatty acids in coconut, babassu, palm kernel oils have the ability to make soap that remains fairly soluble in salty water. That's why salt-based soap recipes have a high percentage of one or more of these particular fats.
Soap made from fats higher in palmitic, stearic, oleic, linoleic and linolenic fatty acids become almost completely insoluble in salty water. These fats include lard, tallow, palm, nut butters, olive oil, and other liquid oils.