When growing the software infrastructure for a large-scale scientific project (namely ALeRCE, Automatic Learning for the Rapid Classification of Events), we observed an "internal API hell" phenomenon in which numerous and various API issues coexist and are inextricably interwoven with each other. Driven by this observation, we conducted a set of investigations to help both understand and deal with this complicated and frustrating situation. Through individual interviews and group discussions, our investigation reveals two root causes of the "internal API hell" in ALeRCE, namely (1) an internal API explosion and (2) an increased "churn" of development teams. Given the nature of the system and the software project, each root cause is inherent and unavoidable. To demonstrate our ongoing work on tackling that "hell", we discuss five API issues and their corresponding solutions, i.e., (1) using a multi-view catalog to help discover suitable APIs, (2) using a publish-subscribe channel to assist API versioning management and negotiation, (3) improving the quality of API adoption through example-driven delivery, (4) using operation serialisation to facilitate API development debugging and migration, and (5) enhancing the usability of long and sophisticated machine learning APIs by employing a graphical user interface for API instantiation. We also briefly consider the threats to validity of our project-specific study. On the other hand, we argue that the root causes and issues are likely to recur for other similar systems and projects. Thus, we urge collaborative efforts on addressing this emerging type of "hell" in software development.