Substance of higher latent heat of melting than water, similar melting point
Indeed, it will be hard to find a substitute for water. You might want to look into how ice packs work.

Some of the things that are added to water in such packs include substances to prevent bacterial growth and to prevent the water to become fully liquid. The water thus become a gel.


  Gel packs may be made by adding hydroxyethyl cellulose (Cellusize) or vinyl-coated silica gel.


One factor that you might consider, is that if there is more mass (for example, dissolving something in the water) will provide more substance for the any heat to go to, so that the temperature rise will be slower.

Another, is hydrogen bonds, which are very present in water molecules and which explains its high specific heats (latent heat and heat capacity).

Unfortunately, adding in stuff to the water will tend to disrupt the hydrogen bonds. I haven't tried it, nor can find something to support my next sentence, but I would expect ammonia to be a possible additive. It has a higher specific heat capacity than water and dissolves easily as well since it does not disrupt hydrogen bonds that much due to its molecular structure.

Glucose is also a potential additive since it doesn't disrupt the hydrogen bonds much, but its specific heat is apparently a bit lower than ammonia. I found a site where I could input some parameters and it outputs the heat capacity of the sugar water and the outputs often say that the specific heat capacity is lower than that of ammonia alone (from the same site that michielm mentioned, ammonia has a specific heat capacity of a bit less than 4.6 at $0^oC$).