We present a scalable method to compute exact worst-case end-to-end latency in applications built on the NVIDIA Holoscan SDK, a framework increasingly adopted for soft real-time ML workloads in medical devices, surgical instruments, and robotics. Holoscan applications are structured as directed acyclic graphs of non-preemptible task threads (operators) connected by FIFO queues, where execution depends not only on input availability but also on downstream buffer capacity - an atypical backpressure mechanism not captured by standard dataflow or middleware models. Existing analyses either lack convergence guarantees or rely on restrictive assumptions (e.g., fixed execution times, unit-sized buffers), resulting in overly conservative bounds. We show that Holoscan's scheduling semantics can be faithfully reduced to homogeneous synchronous dataflow graphs (HSDFGs), enabling exact end-to-end latency analysis. Building on this insight, we introduce a dynamic algorithm that computes tight upper bounds on response time across infinite input streams under variable task runtimes and arbitrary buffer sizes. We prove its correctness and convergence, and demonstrate that it outperforms HSDFG model checking with UPPAAL in runtime while avoiding the pessimism of prior Holoscan-specific analyses. Experiments on real Holoscan applications from NVIDIA HoloHub and large synthetic graphs confirm its scalability and precision.