Resource-exhaustion attacks against autoregressive vision-language models (VLMs) typically assume unimodal threat models, treating the image branch as the primary optimization surface while holding user-visible prompts fixed. Even recent loop-centric variants remain confined to this single-channel paradigm, leaving the exploitation of availability unexplored as a cross-modal optimization problem over jointly controllable input surfaces. We introduce Joint Pixel-Prompt Optimization (JPPO), the first compound adversarial framework elevating the visible prompt to a first-class adversarial variable alongside image perturbations. Under a restricted joint-input threat model, JPPO performs coupled, stagewise optimization over both the pixel and prompt surfaces. This produces synergistic cost amplification, mechanistically distinct from loop-dependent failures, exhibiting negligible loop incidence in our experiments. Evaluating five open-source VLM families on MS COCO and ImageNet under an 8/255 infinity-norm budget, JPPO achieves over 4.6x latency and 5.3x energy amplification on Qwen2.5-VL-7B, and over 36.6x latency with 32.7x energy amplification on BLIP-2. This represents the strongest cost amplification among directly compared baselines while requiring substantially fewer optimization iterations. Ablations confirm this amplification arises from multimodal coordination rather than prompt length or isolated modalities. These findings reveal structural blind spots in current VLM serving defenses, motivating cost-aware robustness evaluation as a first-class security requirement for multimodal deployments.

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