Combinatorial reconfiguration studies how one solution of a combinatorial problem can be transformed into another. The transformation can only make small local changes and may not leave the solution space. An important example is the independent set reconfiguration (ISR) problem, where an independent set of a graph (a subset of its vertices without edges between them) has to be transformed into another one by a sequence of modifications that remove a vertex or add another that is not adjacent to any vertex in the set. The 1st Combinatorial Reconfiguration Challenge (CoRe Challenge 2022) was a competition focused on the ISR problem. The PARIS team participated with two solvers that model the ISR problem as a planning problem and employ different planning techniques for solving it. The solvers successfully competed in the challenge and were awarded 4 first, 3 second, and 3 third places across 9 tracks. In this work, we show how to model ISR problems as planning tasks and describe the planning techniques used by these solvers. For a fair comparison to competing ISR approaches, we re-run the entire competition under equal computational conditions. Besides showcasing the success of planning technology, we hope that this work will create a cross-fertilization of the two research fields.