Public cloud services are integral to modern software development, offering scalability and flexibility to organizations. Based on customer requests, a large product development organization considered migrating the microservice-based product deployments of a large customer to a public cloud provider. We conducted an exploratory single-case study, utilizing quantitative and qualitative data analysis to understand how and why deployment costs would change when transitioning the product from a private to a public cloud environment while preserving the software architecture. We also isolated the major factors driving the changes in deployment costs. We found that switching to the customer-chosen public cloud provider would increase costs by up to 50\%, even when sharing some resources between deployments, and limiting the use of expensive cloud services such as security log analyzers. A large part of the cost was related to the sizing and license costs of the existing relational database, which was running on Virtual Machines in the cloud. We also found that existing system integrators, using the product via its API, were likely to use the product inefficiently, in many cases causing at least 10\% more load to the system than needed. From a deployment cost perspective, successful migration to a public cloud requires considering the entire system architecture, including services like relational databases, value-added cloud services, and enabled product features. Our study highlights the importance of leveraging end-to-end usage data to assess and manage these cost drivers effectively, especially in environments with elastic costs, such as public cloud deployments.