LLMs are increasingly used to support qualitative research, yet existing systems produce outputs that vary widely--from trace-faithful summaries to theory-mediated explanations and system models. To make these differences explicit, we introduce a 4$\times$4 landscape crossing four levels of meaning-making (descriptive, categorical, interpretive, theoretical) with four levels of modeling (static structure, stages/timelines, causal pathways, feedback dynamics). Applying the landscape to prior LLM-based automation highlights a strong skew toward low-level meaning and low-commitment representations, with few reliable attempts at interpretive/theoretical inference or dynamical modeling. Based on the revealed gap, we outline an agenda for applying and building LLM-systems that make their interpretive and modeling commitments explicit, selectable, and governable.