Split Federated Learning (SFL) enables collaborative training between resource-constrained edge devices and a compute-rich server. Communication overhead is a central issue in SFL and can be mitigated with auxiliary networks. Yet, the fundamental client-side computation challenge remains, as back-propagation requires substantial memory and computation costs, severely limiting the scale of models that edge devices can support. To enable more resource-efficient client computation and reduce the client-server communication, we propose HERON-SFL, a novel hybrid optimization framework that integrates zeroth-order (ZO) optimization for local client training while retaining first-order (FO) optimization on the server. With the assistance of auxiliary networks, ZO updates enable clients to approximate local gradients using perturbed forward-only evaluations per step, eliminating memory-intensive activation caching and avoiding explicit gradient computation in the traditional training process. Leveraging the low effective rank assumption, we theoretically prove that HERON-SFL's convergence rate is independent of model dimensionality, addressing a key scalability concern common to ZO algorithms. Empirically, on ResNet training and language model (LM) fine-tuning tasks, HERON-SFL matches benchmark accuracy while reducing client peak memory by up to 64% and client-side compute cost by up to 33% per step, substantially expanding the range of models that can be trained or adapted on resource-limited devices.