(For other readers, halite is just rock salt.)
Your guess about what's happening sounds very reasonable. I can't think of any other way it could happen. The effect you noticed is probably related to one that other readers have written in about. Sometimes saltwater evaporates faster than purer water. Our guess as to why was that that growing layer of deposited salt stayed wet enough to increase the surface area for evaporation. (http://van.physics.illinois.edu/qa/listing.php?id=1476
If any other readers understand the effects of salt on the water-glass surface tension well enough to explain this, we'd love to hear the story.
As for the fluffy crystals, that's not a rare effect. Say that some crystals have started to form. The parts that are most easily reached by further salt ions tend to be the ones that stick out into the solution. That promotes fluffy growth at the tips, leaving gaps behind. Discussions of such effects can be found under the name "diffusion limited aggregation".
p.s. I'm trying this experiment at home. The salt layer on the glass has climbed up about 1cm above the starting level in a day. I guess that strong wetting of that rough salt layer keeps a thin layer of water covering it and extending just beyond it. Rapid evaporation from that exposed layer would lead to depositing more salt, including just above the old salt. This drives the layer gradually up. There's one key aspect that's explainable by equilibrium effects- the coating of the salt layer by solution, just due to surface tension effects. Another key aspect is strongly out of equilibrium- the salt crystals stick to the glass where they form, rather than falling down. That's all just an educated guess.
p.p.s. After a few days some of the salt crept up several cm, over the edge of the glass. That salt layer remains fluffy, unlike the crystals at the bottom of the glass. Although the evidence really isn't any different from what you already reported, just seeing it directly makes me more sure that the explanation is along the lines we mentioned. There must be a "wetting transition", in which the sum of the saltwater-air surface tension and the salt-saltwater surface tension is less than the salt-air surface tension. Under those circumstances, the salt will stay coated with a thin saltwater layer, leaving the effects we discussed.
(published on 03/06/2012)