The paper explores the performance of LLMs in the context of multi-dimensional analytic writing assessments, i.e. their ability to provide both scores and comments based on multiple assessment criteria. Using a corpus of literature reviews written by L2 graduate students and assessed by human experts against 9 analytic criteria, we prompt several popular LLMs to perform the same task under various conditions. To evaluate the quality of feedback comments, we apply a novel feedback comment quality evaluation framework. This framework is interpretable, cost-efficient, scalable, and reproducible, compared to existing methods that rely on manual judgments. We find that LLMs can generate reasonably good and generally reliable multi-dimensional analytic assessments. We release our corpus and code for reproducibility.