Leveraging Graphics Processing Units (GPUs) to accelerate scientific software has proven to be highly successful, but in order to extract more performance, GPU programmers must overcome the high latency costs associated with their use. One method of reducing or hiding this latency cost is to use asynchronous streams to issue commands to the GPU. While performant, the streams model is an invasive abstraction, and has therefore proven difficult to integrate into general-purpose libraries. In this work, we enumerate the difficulties specific to library authors in adopting streams, and present recent work on addressing them. Finally, we present a unified asynchronous programming model for use in the Portable, Extensible, Toolkit for Scientific Computation (PETSc) to overcome these challenges. The new model shows broad performance benefits while remaining ergonomic to the user.