Representing and reasoning about uncertainty is crucial for autonomous agents acting in partially observable environments with noisy sensors. Partially observable Markov decision processes (POMDPs) serve as a general framework for representing problems in which uncertainty is an important factor. Online sample-based POMDP methods have emerged as efficient approaches to solving large POMDPs and have been shown to extend to continuous domains. However, these solutions struggle to find long-horizon plans in problems with significant uncertainty. Exploration heuristics can help guide planning, but many real-world settings contain significant task-irrelevant uncertainty that might distract from the task objective. In this paper, we propose STRUG, an online POMDP solver capable of handling domains that require long-horizon planning with significant task-relevant and task-irrelevant uncertainty. We demonstrate our solution on several temporally extended versions of toy POMDP problems as well as robotic manipulation of articulated objects using a neural perception frontend to construct a distribution of possible models. Our results show that STRUG outperforms the current sample-based online POMDP solvers on several tasks.