Transformer-based \emph{large language models} (LLMs) exhibit remarkable generative capabilities, but their inference throughput is limited by the autoregressive decoding process, which generates only one token per iteration. \emph{Speculative decoding} mitigates this bottleneck by using a lightweight \emph{draft language model} (DLM) to generate multiple draft tokens, which are then verified in parallel by a more accurate \emph{target language model} (TLM). To accommodate the differing computational patterns of the DLM and TLM, prior work has leveraged heterogeneous systems combining xPUs and processing-in-memory (PIM) units to offload compute- and memory-intensive operators, respectively.

However, existing systems often adopt a fixed draft sequence length, leading to excessive rejection of draft tokens during verification—especially under large-batch scenarios—resulting in redundant computation and reduced efficiency. This paper proposes a \emph{runtime adaptive draft length} adjustment technique that dynamically tailors the draft length for each request by monitoring cumulative acceptance probabilities, thereby minimizing the generation and verification of invalid tokens. Yet, integrating adaptive draft lengths into existing PIM-enabled heterogeneous systems introduces two new challenges: (1) sequential execution of the DLM and TLM becomes inefficient due to synchronization bubbles caused by request-wise variability in draft lengths, and (2) static operator mappings become suboptimal as draft length variability alters operator arithmetic intensities dynamically. To address these issues, we introduce \textbf{SADDLE}, a PIM-enabled heterogeneous system designed to exploit adaptive draft lengths effectively. SADDLE incorporates two key mechanisms: (1) an \emph{asynchronous speculative decoding pipeline} that decouples DLM prediction and TLM verification to reduce idle time, and (2) an \emph{arithmetic intensity-aware operator scheduler} that dynamically assigns operators to the most suitable hardware units. Experimental results show that SADDLE achieves average speedups of 2.88$\times$ over a state-of-the-art GPU-only solution and 1.71$\times$ over the best-performing GPU+PIM baseline.