Recent advancements in Large Language Model (LLM)-based Natural Language Generation evaluation have largely focused on single-example prompting, resulting in significant token overhead and computational inefficiencies. In this work, we introduce BatchGEMBA-MQM, a framework that integrates batched prompting with the GEMBA-MQM metric for machine translation evaluation. Our approach aggregates multiple translation examples into a single prompt, reducing token usage by 2-4 times (depending on the batch size) relative to single-example prompting. Furthermore, we propose a batching-aware prompt compression model that achieves an additional token reduction of 13-15% on average while also showing ability to help mitigate batching-induced quality degradation. Evaluations across several LLMs (GPT-4o, GPT-4o-mini, Mistral Small, Phi4, and CommandR7B) and varying batch sizes reveal that while batching generally negatively affects quality (but sometimes not substantially), prompt compression does not degrade further, and in some cases, recovers quality loss. For instance, GPT-4o retains over 90% of its baseline performance at a batch size of 4 when compression is applied, compared to a 44.6% drop without compression. We plan to release our code and trained models at https://github.com/NL2G/batchgemba to support future research in this domain.