|MadSci Network: Biochemistry|
As you appear to understand very well, the key to understanding sugar crystals and glasses is hydrogen bonding and the interaction with included water.
Anything which also interacts with water, either ionically (electrostatically by charges) or by hydrogen bonding (weak electrostatic effects), or with the sugar, can disrupt the configuration or retard crystallization. Sugar syrups often include an acid (lemon juice or citric acid) to prevent crystallization. As you indicate, acid hydrolysis can break apart sucrose into its two monosaccharide elements (glucose and fructose). An enzyme (invertase) can do the same.
Certain compounds can interact directly with sugars. This includes acetates, citrates and tartrates.
Milkiness is a sign of scattering of light due to formation of amorphous polymers. Slime formed by bacteria is mucopolysaccharides, or polymers of simple sugars.
I don't know for sure the answer to your question, but I would guess that NaCl is more disruptive of the sugar crystallization or glassification structure, and so results in amorphous scattering. The tartrate might be more compatible with regularity in the structure and results in a more ordered state that is not milky.
You might try the same experiment with acetates and citrates, which should behave similar to tartrates. Compare with bromide, nitrate and sulfate as inorganic salts. You can also try the effects of divalent or trivalent cations, such as calcium, magnesium and aluminum salts.
Congratulations for your deep understanding of sugar chemistry at such an early age. The principles involved will explain much of biochemistry, including protein chemistry.
Try the links in the MadSci Library for more information on Biochemistry.