End-to-end full-duplex Speech Language Models (SLMs) require precise turn-taking for natural interaction. However, optimizing temporal dynamics via standard raw-token reinforcement learning (RL) degrades semantic quality, causing severe generative collapse and repetition. We propose ASPIRin, an interactivity-optimized RL framework that explicitly decouples when to speak from what to say. Using Action Space Projection, ASPIRin maps the text vocabulary into a coarse-grained binary state (active speech vs. inactive silence). By applying Group Relative Policy Optimization (GRPO) with rule-based rewards, it balances user interruption and response latency. Empirical evaluations show ASPIRin optimizes interactivity across turn-taking, backchanneling, and pause handling. Crucially, isolating timing from token selection preserves semantic coherence and reduces the portion of duplicate n-grams by over 50% compared to standard GRPO, effectively eliminating degenerative repetition.