Applications that fuse machine learning and simulation can benefit from the use of multiple computing resources, with, for example, simulation codes running on highly parallel supercomputers and AI training and inference tasks on specialized accelerators. Here, we present our experiences deploying two AIguided simulation workflows across such heterogeneous systems. A unique aspect of our approach is our use of cloud-hosted management services to manage challenging aspects of crossresource authentication and authorization, function-as-a-service (FaaS) function invocation, and data transfer. We show that these methods can achieve performance parity with systems that rely on direct connection between resources. We achieve parity by integrating the FaaS system and data transfer capabilities with a system that passes data by reference among managers and workers, and a user-configurable steering algorithm to hide data transfer latencies. We anticipate that this ease of use can enable routine use of heterogeneous resources in computational science.