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Lexical exact match systems that use inverted lists are a fundamental text retrieval architecture. A recent advance in neural IR, COIL, extends this approach with contextualized inverted lists from a deep language model backbone and performs retrieval by comparing contextualized query-document term representation, which is effective but computationally expensive. This paper explores the effectiveness-efficiency tradeoff in COIL-style systems, aiming to reduce the computational complexity of retrieval while preserving term semantics. It proposes COILcr, which explicitly factorizes COIL into intra-context term importance weights and cross-context semantic representations. At indexing time, COILcr further maps term semantic representations to a smaller set of canonical representations. Experiments demonstrate that canonical representations can efficiently preserve term semantics, reducing the storage and computational cost of COIL-based retrieval while maintaining model performance. The paper also discusses and compares multiple heuristics for canonical representation selection and looks into its performance in different retrieval settings.