Discrete choice models are useful to understand how decisions are made and to predict future choices. However, most applications rely on several simplifying assumptions. In this paper we relax one of them, that choice consistency (reflected by the scale parameter) is uniform across all individuals and choices. For this, we introduce a heterogeneous scale hybrid choice model that integrates latent cognitive effort and survey engagement, along with observed information processing behaviour, to explain scale heterogeneity. We use data obtained applying a Design of Designs (DoD) stated choice survey, systematically varying task complexity (number of alternatives and number of attributes) and the choice context (route selection, holiday destination, and residential location). Our findings reveal that both cognitive effort and survey engagement significantly influence the scale factor, and thus choice consistency. Further, the impact of cognitive effort depends on context: for example, in high-reversibility, routine contexts, higher reported effort relates to lower consistency, whereas in low-reversibility, high-stakes residential choices, greater effort (supported by an interactive map-based decision aid) is associated with higher consistency. We also show that scale heterogeneity is driven by perceived complexity, which leads to choice simplification strategies like selective information processing. Finally, our results highlight the dynamic relationship between survey design, cognitive processes and choice consistency, with significant implications for designing more effective stated choice surveys and decision support tools.