Large language models (LLMs) are increasingly capable of simulating human behavior, offering cost-effective ways to estimate user responses to various surveys and polls. However, the questions in these surveys usually reflect socially understood attitudes: the patterns of attitudes of old/young, liberal/conservative, as understood by both members and non-members of those groups. It is not clear whether the LLM binding is \emph{deep}, meaning the LLM answers as a member of a particular in-group would, or \emph{shallow}, meaning the LLM responds as an out-group member believes an in-group member would. To explore this difference, we use questions that expose known in-group/out-group biases. This level of fidelity is critical for applying LLMs to various political science studies, including timely topics on polarization dynamics, inter-group conflict, and democratic backsliding. To this end, we propose a novel methodology for constructing virtual personas with synthetic user "backstories" generated as extended, multi-turn interview transcripts. This approach is justified by the theory of \emph{narrative identity} which argues that personality at the highest level is \emph{constructed} from self-narratives. Our generated backstories are longer, rich in detail, and consistent in authentically describing a singular individual, compared to previous methods. We show that virtual personas conditioned on our backstories closely replicate human response distributions (up to an 87% improvement as measured by Wasserstein Distance) and produce effect sizes that closely match those observed in the original studies of in-group/out-group biases. Altogether, our work extends the applicability of LLMs beyond estimating socially understood responses, enabling their use in a broader range of human studies.