I think your methodology is a bit wrong. When the frozen brine melts into the water, the water won't be 100% water anymore. So, the specific heat capacity of the water changes, making the change in temperature different. Maybe that's why you have a 25% drop when compared to water. You can follow the steps below only if you have a heat source that generates a known amount of heat(energy), like an immersion heater with known voltage and wattage.
1. Weigh an empty container
2. Clamp a filter funnel to a retort stand (or anything that can hold it off the table surface)
3. Place the container below the filter funnel
4. Dry the ice and crush it
5. 108
Place the crushed ice into the filter funnel
6. Set a timer for a specific amount of time, place the heater into the crushed ice and turn the power on, start the timer at the same time.
7. Once the time is up, switch off the power to the heater and remove the container
8. Now, weigh the container with the melted ice
9. Use the same set up and follow the same steps in the steps above, but this time, don't turn on the heater (but still leave it in the ice) (this is to find the amount of ice that melted due to the room temperature)
10. Find the mass of ice that melted due to the heater by subtracting the mass of the container and melted ice without the heater on from the mass of the container and melted ice with the heater on
11. Find the amount of heat generated from the heater by taking the power rating of the heater (in Watts) and multiply it by the time the ice melted for.
The main equation you'll use is ML = Pt, where M is the mass of ice that melted due to the heater, L is the specific latent heat of fusion, P is the power rating of the heater in Watts and t is the time that you let the ice melt for. From there I think you can figure out L. All this is done with the assumption that the heat from the heater that is lost to the surroundings is 0 or negligible.
As for the "mushy" ice, you probably didn't let it freeze long enough.
IDK if any of this will help now though, cus it's been more than 5 years, and I'm pretty sure you're done with the experiment.LOL 108