First-come first-serve scheduling can result in substantial (up to 10%) of transiently idle nodes on supercomputers. Recognizing that such unfilled nodes are well-suited for deep neural network (DNN) training, due to the flexible nature of DNN training tasks, Liu et al. proposed that the re-scaling DNN training tasks to fit gaps in schedules be formulated as a mixed-integer linear programming (MILP) problem, and demonstrated via simulation the potential benefits of the approach. Here, we introduce MalleTrain, a system that provides the first practical implementation of this approach and that furthermore generalizes it by allowing it use even for DNN training applications for which model information is unknown before runtime. Key to this latter innovation is the use of a lightweight online job profiling advisor (JPA) to collect critical scalability information for DNN jobs -- information that it then employs to optimize resource allocations dynamically, in real time. We describe the MalleTrain architecture and present the results of a detailed experimental evaluation on a supercomputer GPU cluster and several representative DNN training workloads, including neural architecture search and hyperparameter optimization. Our results not only confirm the practical feasibility of leveraging idle supercomputer nodes for DNN training but improve significantly on prior results, improving training throughput by up to 22.3\% without requiring users to provide job scalability information.