Free-text responses are commonly collected in psychological studies, providing rich qualitative insights that quantitative measures may not capture. Labeling curated topics of research interest in free-text data by multiple trained human coders is typically labor-intensive and time-consuming. Though large language models (LLMs) excel in language processing, LLM-assisted labeling techniques relying on closed-source LLMs cannot be directly applied to free-text data, without explicit consent for external use. In this study, we propose a framework of assembling locally-deployable LLMs to enhance the labeling of predetermined topics in free-text data under privacy constraints. Analogous to annotation by multiple human raters, this framework leverages the heterogeneity of diverse open-source LLMs. The ensemble approach seeks a balance between the agreement and disagreement across LLMs, guided by a relevancy scoring methodology that utilizes embedding distances between topic descriptions and LLMs' reasoning. We evaluated the ensemble approach using both publicly accessible Reddit data from eating disorder related forums, and free-text responses from eating disorder patients, both complemented by human annotations. We found that: (1) there is heterogeneity in the performance of labeling among same-sized LLMs, with some showing low sensitivity but high precision, while others exhibit high sensitivity but low precision. (2) Compared to individual LLMs, the ensemble of LLMs achieved the highest accuracy and optimal precision-sensitivity trade-off in predicting human annotations. (3) The relevancy scores across LLMs showed greater agreement than dichotomous labels, indicating that the relevancy scoring method effectively mitigates the heterogeneity in LLMs' labeling.