Microservices are a dominant architecture in cloud computing, offering scalability and modularity, but also posing complex deployment challenges. As data centers contribute significantly to global carbon emissions, carbon-aware scheduling has emerged as a promising mitigation strategy. However, most existing solutions target batch, high-performance, or serverless workloads and assume access to global-scale infrastructure. Such an assumption does not hold for many national or regional small to medium-sized enterprises (SMEs) with microservice applications, which represent the real-world majority. In this paper, we present HuntMS, an Adaptive Carbon and Efficiency-aware placement for microservices that considers carbon, cost, and latency constraints. HuntMS dynamically places microservices across geographically constrained regions using a scalable optimization strategy that leverages insight-based search space pruning techniques. Evaluation on a real-world deployment shows that HuntMS quickly adapts to real-time changes in workload and carbon intensity and reduces carbon emissions by 37.4% and operational cost by 3.6%, on average, compared to a static deployment within a single country, while consistently meeting SLOs. In this way, HuntMS enables carbon- and cost-aware microservice deployment for latency-sensitive applications in regionally limited infrastructures for SMEs.