This paper presents range-based 6-DoF Monte Carlo SLAM with a gradient-guided particle update strategy. While non-parametric state estimation methods, such as particle filters, are robust in situations with high ambiguity, they are known to be unsuitable for high-dimensional problems due to the curse of dimensionality. To address this issue, we propose a particle update strategy that improves the sampling efficiency by using the gradient information of the likelihood function to guide particles toward its mode. Additionally, we introduce a keyframe-based map representation that represents the global map as a set of past frames (i.e., keyframes) to mitigate memory consumption. The keyframe poses for each particle are corrected using a simple loop closure method to maintain trajectory consistency. The combination of gradient information and keyframe-based map representation significantly enhances sampling efficiency and reduces memory usage compared to traditional RBPF approaches. To process a large number of particles (e.g., 100,000 particles) in real-time, the proposed framework is designed to fully exploit GPU parallel processing. Experimental results demonstrate that the proposed method exhibits extreme robustness to state ambiguity and can even deal with kidnapping situations, such as when the sensor moves to different floors via an elevator, with minimal heuristics.