Quadratic Surveys (QSs) elicit more accurate preferences than traditional methods like Likert-scale surveys. However, the cognitive load associated with QSs has hindered their adoption in digital surveys for collective decision-making. We introduce a two-phase "organize-then-vote" QS to reduce cognitive load. As interface design significantly impacts survey results and accuracy, our design scaffolds survey takers' decision-making while managing the cognitive load imposed by QS. In a 2x2 between-subject in-lab study on public resource allotment, we compared our interface with a traditional text interface across a QS with 6 (short) and 24 (long) options. Two-phase interface participants spent more time per option and exhibited shorter voting edit distances. We qualitatively observed shifts in cognitive effort from mechanical operations to constructing more comprehensive preferences. We conclude that this interface promoted deeper engagement, potentially reducing satisficing behaviors caused by cognitive overload in longer QSs. This research clarifies how human-centered design improves preference elicitation tools for collective decision-making.