In reinforcement learning (RL), it is often advantageous to consider additional constraints on the action space to ensure safety or action relevance. Existing work on such action-constrained \ac{RL} faces challenges regarding expressive policy updates, computational efficiency, and predictable runtime. Recent work proposes to use truncated normal distributions for stochastic policy gradient methods. However, the computation of key characteristics, such as the entropy, log-probability, and their gradients, becomes intractable under complex constraints. Hence, prior work approximates these using the non-truncated distributions, which severely degrades performance. We argue that accurate estimation of these characteristics is crucial in the action-constrained \ac{RL} setting, and propose efficient numerical approximations for them. We also provide an efficient sampling strategy for truncated policy distributions and validate our approach on three benchmark environments, which demonstrate significant performance improvements when using accurate estimations.