What is "White Moist Sugar"?

My guess is that "white moist sugar" is meant literally -- that is, white sugar that is not completely dry.

Granulated white sugar starts out wet, and is dried as the last step in the modern production process. At the time, sugar was sold in "loaves", which could be cut into pieces or more finely ground, rather than the hot-air convection process used these days. Drying would likely be seen as important for granulated sugar served in a sugar bowl with tea, but wouldn't matter for sugar to be used in baking -- except that it would affect the weight.

So at a guess, you'd want to just mix a bit of water into sugar until it clumped together slightly, and use half a pound of the result.