This is not a text book answer, more of a logic answer. Cold water at 4 degrees C is at its densest so it goes to the bottom of stream or lake. Colder water than 4 degrees C is less dense at eventually freezes if cold enough. Salt water has more ions and it is denser than freshwater and you will get a wedge effect when salt water is introduced up freshwater channels. So it appears that the heavier ionic water will stay in in the water column unless well mixed. So if that all makes sense, the low ionic water must freeze faster as it is lower density and rises above higher ionic waters and as the lower ionic waters near the surface cools to temperatures lower than 4 degrees C, it is the first to freeze and must freeze faster. It is an interesting question and deductive reasoning does not always work, so either a textbook answer or confirmation from a few others would be appropriate. If you fish on an ice lake in the winter, take a sample of the ice and melt it and see if it is not a somewhat lower ionic strength (conductivity) than the lake water at various depths.
I am semi-retired, no lab, funding, or position of influence to carry on research as you are suggesting. 40 plus years ago I had the lab and energy to chase a few ideas like Indiana Jones. I may have relinquish to your youth, position and energy, and will celebrate your accomplishment when you figure it out. It would be interesting to set this up. I am sure you have heard of the sea level rise, glacial disappearances diluting sea water salinity and fresh water can float over salt water, so the circulation pattern of the ocean could freeze or reduce effectiveness, creating climate shifts. There are potential applications to a question like yours. Ice damage in breakup is a big issue. If we could figure out ways to break it up and melt before severe floods with icejam damage events or to improve transport safety in specific shipping lanes or ocean circulation areas, who knows it may win a nobel, or at least recognition of some sort. I am not a marine scientist, and I am sure you are just being facetious in suggesting cooperative effort for a nobel, but I appreciate the offer, and do some limited cooperation, but I can only do so much volunteering before I no business. I am serious though, your question may be important to consider for increased understanding and potential applications.