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Generalized planning aims to learn policies that generalize across collections of instances within a classical planning domain. Recent Graph Neural Network (GNN) approaches have learned nearly perfect policies for several domains. This work improves on the recently published idea of Iterated Width (IW) policies. Therein, the policy broadens its successor scope through an IW-lookahead search that can "jump" over multiple transitions, simplifying the problem structure. Yet, each transition is evaluated individually, leading to unscalable compute costs and expressivity limitations. Furthermore, although IW(1) is attractive because it scales linearly with the number of atoms, it becomes inefficient once thousands of objects are considered, as in the International Planning Competition (IPC) 2023 benchmark. We address both limitations. First, we introduce a vastly more efficient holistic encoding of the entire search tree. It jointly represents IW(1)-reachable states only by their relational differences to the current state, enabling Relational GNNs (R-GNNs) to score all transitions in a single forward pass. Second, we define Abstracted IW(1) to improve scaling through relational abstraction during novelty checks. Rather than testing fully instantiated atoms, it abstracts each atom by replacing all but one argument with its type. The original atom is novel if any of its abstracted forms is novel. This structural compression shifts novelty search scaling from atoms to objects, while preserving meaningful subgoal structure. We evaluate our contributions on the hyperscaling IPC 2023 benchmark and across diverse domains, including domains requiring features beyond the $C_2$ logic fragment. Our policies achieve new state-of-the-art performance, significantly surpassing prior work, including the classical planner LAMA.